Created by: Tonya Jagoe

Measures of Central Tendency mean median mode

Measures of Spread range Variance of population Standard deviation For Sample - divide by (n-1) instead of n.

Measures of Central Tendency & Spread Input the data for these test scores into your calculator to find requested statistics. Step 1: STAT, EDIT Step 2: data in L 1 Step 3: STAT, CALC Step 4: 1-Var Stats, L 1 enterStep 5: Must scroll down to see all statistics.

Measures of Central Tendency & Spread Input the data for these test scores into your calculator to find the following statistics. Mean = µ or Sum of x’s = ∑ Sample standard deviation = Sx Population standard deviation = σx Minimum Value = minX = Quartile 1 = Q1= Median = Med = Quartile 3 = Q3 = Maximum Value = maxX = Interquartile Range = Q3 – Q1 Range = Max - Min Sample Variance = (Sx) 2 Population Variance = (σx) 2 =77.8 Mean and standard deviation should be rounded to one more decimal place than the original data. ONLY use original values to calculate any other values. =2645 =10.2 = = 18 = 37 = = These come directly from your calculator… Calculate these… (mu) (lowercase sigma)

Box Plot - 5 number summary Minimum Value = minX = Quartile 1 = Q1= Min Max Quartile 3 = Q3 = Maximum Value = maxX = Median = Med = Med of lower half Q1 Med Q2 Med of upper half Q3 Step 1: Draw a number line that extends below the “MIN” and above the “MAX” Step 2: Draw lines above number line for each of the components of the 5-number summary. Step 3: Draw boxes to connect Q1 and Q3 both back to the Median. Step 4: Draw lines to connect the Min and the Max to the nearest box.

Box Plot – using Calculator Outliers are data that lie more than 1.5 times IQR beyond Q3 or Q1. There are no outliers in this data set. To verify: Step 1: data in L 1 Step 2: STATPLOT (2 nd y=); #1 Step 3: ON; Type: 4 th choice (shows outliers); Xlist: L1; Freq: 1; Mark: 1 st choice; Step 4: ZOOM; 9:ZOOMSTAT Step 5: Enter to see box plot Step 6: TRACE; right arrow to see next value IQR = 181.5(IQR) = 1.5(18) = 27 Q1-27 = = 42 Q3+27 = = 114 No data above 114 or below 42, therefore, NO OUTLIERS

Standard Deviation - Distribution Mean = µ or =77.8 = or Mean (µ) ± 1 std. dev. (σ) Mean (µ) ± 2 std. dev. (σ) Most scores will fall within 1 standard deviation. Almost all will fall within 2 standard deviations. As far as we know, this is the population data, test scores for everyone who took test. If the scores were being compared to other classes, this would be a sample and we would use sample statistics. Population standard deviation = σx (10.1) - 2(10.1) Step 1: Draw a number line. Step 2: Draw line above for Mean. Step 4: Subtract 1 std. dev. from mean – draw line. Step 5: Draw arrows connecting mean and lines. Mean (µ) ± 1 std. dev. (σ) Step 3: Add 1 std. dev. to mean – draw line. Step 1: Draw a number line. Step 2: Draw line below for Mean. Step 4: Subtract 2 std. dev’s. from mean – draw line. Step 5: Draw arrows connecting mean and lines. Mean (µ) ± 2 std. dev. (σ) Step 3: Add 2 std. dev’s. to mean – draw line.