Mean, Median, and Mode of Ungrouped Data Section 2.5

Mean - Ungrouped

Median - Ungrouped No formula – BUT, we do use a “position locator” formula to show us where to begin to find the median in the cumulative frequency column. (cf) Position Locator:

Cumulative Frequency - cf The cumulative frequency is a column which keeps a running total of the frequencies. Ex: fcf n =100

Mode Find the number with the greatest frequency (f) and read the “x” value. This is the mode of the set or the value that occurs the most often.

Example Find the mean, median, and mode of the following data. xf n=24

Put “x” in L1 and “f” in L2.

In L3 set a formula for

You should see this….L3 shows (f)(x).

On your chart – not in calculator – add a column for cf. xffxcf n=2473

Find the mean….

Find the median…… n/2 = 24/2 = 12 Locate the class containing the 12 th value in the set in the cumulative frequency column.

The 12 th position is after 11 th and before 16 th ……… xffxcf n=24

Now, read the x value that corresponds to the 12 th position…. The median is 3. xffxcf n=24

Find the mode……. Locate the highest frequency and read the x value that corresponds. NOTE: The mode is not the frequency, it is the x that corresponds to that frequency.

The largest frequency is “8”… xffxcf n=24

The mode is 2. xffxcf n=24

Now, you try……… Find the mean, median, and mode of the following set of data. xf

This is the chart you should have…….. xffxcf

The mean……

The median……. n/2 = 50/2 = 25 xffxcf

The mode…….. xffxcf

Now, use the calculator….. Put “x’s” in L1 and frequencies in L2. Press “Stat”, Calc, One-Var stats, L1, L2 and then enter. The next slide will show the keystrokes necessary.

Keystrokes….

Screen shows mean. Median can be found as you scroll down…..

Variance and St. Deviation – Ungrouped Section 2.5

Variance Formula - Ungrouped

Standard Deviation Formula….

Example - Ungrouped Find the variance and standard deviation of the set. xf n=25

Calculator Lists……. Put x’s in L1 and f’s in L2. Then set a formula to find f (x).

Finding f times x squared…. Set a formula in L4

This is what your columns should look like…… xffxf (x squared) n=

Find the variance.

Find the standard deviation.

Now you try… Find the variance and standard deviation of the set. xf n=24

Your lists should look like this….. xffxf (x squared) n=

Find variance.

Find the standard deviation.

Calculator Only….. Put x’s in L1 and f’s in L2. Press Stat, Calc, One-var stats, L1,L2 enter

Homework Make sure that you do all the homework BY HAND using the columns. After you finish, you can check your answers using your calculator.