LET’S WATCH THE 3 O’CLOCK PARADE Sample 1 Spectator Area Parade route two miles in length with spectators ten feet deep on both side. Sample 2 Sample 5 S1 = 11 people 2. Sample area: 5 x 5 squares Sample 1 (S1) = 11 people S2 = 16 people S5 = 4 people Sample 2 (S2) = 16 people Parade Route Parade Route Sample 3 (S3) = 27 people Sample 4 (S4) = 17 people Sample 3 Sample 5 (S5) = 4 people Sample Area: The physical area or space containing a sample population. Sample 4 S3 = 27 people Spectator Area S4 = 17 people

LET’S WATCH THE 3 O’CLOCK PARADE Sample 1 Sample 1 Sample 2 Sample 3 Sample 4 Sample 5 Spectator Area Parade route two miles in length with spectators ten feet deep on both side. Sample 2 Sample 5 S1 = 11 people = 11 people S2 = 16 people S3 = 27 people S4 = 17 people S5 = 4 people S1 2. Sample area: 5 x 5 squares Sample 1 (S1) = 11 people S2 = 16 people S5 = 4 people Sample 2 (S2) = 16 people Parade Route Parade Route Sample 3 (S3) = 27 people Sample 4 (S4) = 17 people Sample 3 Sample 5 (S5) = 4 people Sample Area: The physical area or space containing a sample population. Sample 4 S3 = 27 people Spectator Area S4 = 17 people

LET’S WATCH THE 3 O’CLOCK PARADE Sample 1 Sample 2 Sample 3 Sample 4 Sample 5 Sample Mean Parade route two miles in length with spectators ten feet deep on both side. = S1 = 11 people S2 = 16 people S3 = 27 people S4 = 17 people S5 = 4 people 15 (people) 2. Sample squares: 5 x 5 11 + 16 + 27 + 17 + 4 = 75 Sample 1 (S1) = 11 people Sample 2 (S2) = 16 people Sample (population): A segment or portion of a population used to suggest or represent the characteristics of the entire population. Sample 3 (S3) = 27 people Sample 4 (S4) = 17 people Sample 5 (S5) = 4 people Sample mean: The sample mean (sometimes referred to as the arithmetic average) is an estimate of the population mean calculated from a group of observations by dividing the sample population by the number of samples. Sample = 75 people Sample mean = 15 people 75 people 75 15 __ The sample mean is 15 (people). _________ = = 5 samples 5

LET’S WATCH THE 3 O’CLOCK PARADE Sample 1 Sample 2 Sample 3 Sample 4 Sample 5 Sample Mean Parade route two miles in length with spectators ten feet deep on both side. = S1 = 11 people S2 = 16 people S3 = 27 people S4 = 17 people S5 = 4 people 15 (people) 2. Sample squares: 5 x 5 11 + 16 + 27 + 17 + 4 = 75 Sample 1 (S1) = 11 people Sample 2 (S2) = 16 people Sample (population): A segment or portion of a population used to suggest or represent the characteristics of the entire population. Sample 3 (S3) = 27 people Sample 4 (S4) = 17 people Sample 5 (S5) = 4 people Sample mean: The sample mean (sometimes referred to as the arithmetic average) is an estimate of the population mean calculated from a group of observations by dividing the sample population by the number of samples. Sample (SP) = 75 people Sample mean = 15 people 75 people 75 15 ppl __ The sample mean is 15 (people). _________ = = 5 samples 5

LET’S WATCH THE 3 O’CLOCK PARADE Sample 1 Sample 2 Sample 3 Sample 4 Sample 5 Sample Mean Parade route two miles in length with spectators ten feet deep on both side. = S1 = 11 people S2 = 16 people S3 = 27 people S4 = 17 people S5 = 4 people 15 people 2. Sample squares: 5 x 5 SD = 15 people per 25 sq. ft. Sample 1 (S1) = 11 people Sample 2 (S2) = 16 people Sample Area: The physical area or space containing a sample population. Sample 3 (S3) = 27 people 5 ft. x 5 ft = 25 sq. ft. NOTE: We use square feet because we are multiplying by a second dimension. Sample 4 (S4) = 17 people Sample 5 (S5) = 4 people Sample Density: A measurement of a sample (population) per unit area or unit volume. It is a quantity of type number density most frequently applied to living organisms, especially humans, though it can also be applied to non-living objects. Sample (SP) = 75 people Sample mean = 15 people Since the sample mean is 15 people and the sample area is 25 square feet, Sample density: SD = 15 people / 25 sq. ft. the average sample density is 15 people per 25 square feet.

LET’S WATCH THE 3 O’CLOCK PARADE 1. Sample area: 25 sq. ft. What do we know? 1. Sample area: 25 sq. ft. (5 ft. x 5 ft.) 2. Sample mean: 15 people 2. Sample mean = 15 people 3. Sample density: SD = 15 people / 25 sq. ft. 3. Sample density: SD = 15 people per 25 sq. ft. 4. Parade spectator population area is two miles in length and ten feet deep on both sides 4. Parade route two miles in length with spectators ten feet deep on both sides. = 42,240 sq. ft. NOTE: Again, We use square feet because we are multiplying by a second dimension. The spectator population area for the parade route Since the parade route is two miles in length and ten-feet deep on both sides, the spectator population area is = 42,240 sq. ft. 42,240 sq. ft. 1 mile = 5,280 feet Because the spectator area is 10 feet deep but the sample area is 5 feet by deep. 5,280 feet x 2 = 10,560 feet x 2 = 21,120 sq. ft x 2 = 42,240 sq. ft Because the parade route is two miles in length Because spectator are on both sides of the parade.

LET’S WATCH THE 3 O’CLOCK PARADE 1. Sample area: 25 sq. ft. What do we know? 1. Sample area: 25 sq. ft. (5 ft. x 5 ft.) 2. Sample mean: 15 people 2. Sample mean = 15 people 3. Sample density: SD = 15 people / 25 sq. ft. 3. Sample density: SD = 15 people per 25 sq. ft. 4. Parade spectator population area is two miles in length and ten feet deep on both sides 4. Parade route two miles in length with spectators ten feet deep on both sides. = 42,240 sq. ft. NOTE: Again, We use square feet because we are multiplying by a second dimension. The spectator population area for the parade route Since the parade route is two miles in length and ten-feet deep on both sides, the spectator area for the parade is: = 42,240 sq. ft. 42,240 sq. ft. 1 mile = 5,280 feet Because the spectator area is 10 feet deep but the sample area is 5 feet by deep. 5,280 feet x 2 = 10,560 feet x 2 = 21,120 sq. ft x 2 = 42,240 sq. ft Because the parade route is two miles in length Because spectator are on both sides of the parade.

25,344 people attended the parade. LET’S WATCH THE 3 O’CLOCK PARADE 1. Sample area: 25 sq. ft. What do we know? 1. Sample area: 25 sq. ft. (5 ft. x 5 ft.) 2. Sample mean: 15 people 2. Sample mean = 15 people 3. Sample density: SD = 15 people / 25 sq. ft. 3. Sample density: SD = 15 people per 25 sq. ft. 4. Spectator population area: 42,240 sq. ft. 4. The spectator population area for the parade route Since the spectator population area for the parade is 42,240 sq. ft., and the sample area is 25 sq. ft., we can divide the population area by the sample area and multiply by the sample mean to estimate the number of people attending the parade. = 42,240 sq. ft. population area: 42,240 sq. ft. _________________ ___________ 25,344 = 1,689.6 x 15 = 25,344 people attended the parade. sample area: 25 sq. ft. people Sample mean

25,344 people attended the parade. LET’S WATCH THE 3 O’CLOCK PARADE 1. 5 ft. x 5ft. = 25 sq. ft. How did we do that? 2. 11 + 16 + 27 + 17 + 4 = 75 1. Calculate the sample area: Area = length x width 75 2. Calculate sample population: S1 + S2 + S3 + S4 + S5 = SP 3. ___ = 15 5 sample population ____________________ 3. Calculate the sample mean: 4. 1 mile = 5,280 ft # of sample areas Route = 2 miles ______ x 2 10,560 ft Spectators are 10 ft deep x 2 ______ 21,120 sq.ft. 4. Calculate the population area: Area = length x width Spectators on Both sides x 2 ______ 42,240 sq.ft. 5. Divide the population area by the sample area: population area _______________ = 1,689.6 sample area 42,240 sq.ft. 5. _________ = 1,689.6 25 sq.ft. 1,689.6 x Sample mean = The approximate number of people attending the event 6. Multiply by the sample mean: 1,689.6 x 15 = 25,344 6. 25,344 people attended the parade.

LET’S WATCH THE 3 O’CLOCK PARADE What about filling a room with tennis balls, or a carton with golf balls, or a crate with oranges? How d0 we do that? 1. Calculate the sample volume: Volume = length x width x height 2. Calculate sample population: S1 + S2 + S3 + S4 + S5 = SP The only thing we really change is we work with volumes instead of areas. sample population ____________________ 3. Calculate the sample mean: # of sample areas When we talk about three dimensions, we multiply area (length x width) by height, and we look at / talk about volume instead of area. 4. Calculate the population volume: Volume = length x width x height 5. Divide the population volume by the sample volume: population volume _________________ = ? sample volume NOTE: Because volume multiplies 3 dimensions, volume is expressed in cubic units. x = The approximate number of people attending the event 6. Multiply by the sample mean: ? Sample mean

Characteristics of Sample Populations Sample Area: The physical area or space containing a sample population. Characteristics of Sample Populations Sample (population): A segment or portion of a population used to suggest or represent the characteristics of the entire population. Sample mean: The sample mean (also referred to as the arithmetic average) is an estimate of the population mean calculated from a group of observations by dividing the sample population by the number of samples. Sample Density: A measurement of a sample (population) per unit area or unit volume. It is a quantity of type number density most frequently applied to living organisms, especially humans, though it can also be applied to non- living objects. Descriptive Statistics: The quantifiable measures of a sample population: Observations, Range, Median, Q1, Q3, IQR, IQL, Outliers, Min, Max, Mean, and Mode. Standard Deviation: The variance from the mean for a sample population.