Statistic question

Question

Given the following data:
222-233-254-241-251-268-276-220-238-253-249-236-247-256-261-227-257-244-239-242

a) Construct a frequency distribution using 6 classes.

b) Construct a relative frequency distribution from part (a)

c) Draw a histogram for the frequency distribution in part (a)

d) construct a Stem-and-leaf plot for the data listed above

Answer 1

First sort the data (note: if you already have the classes, then this step is unnecessary):

220
222
227
233
236
238
239
241
242
244
247
249
251
253
254
256
257
261
268
276

 

Usually, frequency distributions create meaningful class (but not always of equal size), like ranges of ages or salaries or number of children, etc.  Since we can pick the 6 classes (and the data seems to suggest this), let's select 6 equal groups: 221-230, 231-240, ... 271-180

 

a) With that grouping, the frequency distribution is:

221 - 230      3

231 - 240      4

241 - 250      5

251 - 260      5

261 - 270      2

271 - 280      1

                -----

                   20

Note:  It does help to check that the total of the frequencies is the total number of observations in the data.

 

b) Now, we actually need the count of observations (count of data points), that is 20, because we divide each frequency value by it.

221 - 230      0.15
231 - 240      0.20
241 - 250      0.25
251 - 260      0.25
261 - 270      0.10
271 - 280      0.05
                -----
                    1.00

These decimals represent percents, so they should add up to 100.0%.

 

c)

 

221 - 230      3     XXX
231 - 240      4     XXXX
241 - 250      5     XXXXX
251 - 260      5     XXXXX
261 - 270      2     XX
271 - 280      1     X

 

d)

    stem | leaf

--------------------

      22   |   0 2 7

      23   |   3 6 8 9

      24   |   1 2 4 7 9

      25   |   1 3 4 6 7

      26   |   1 8

      27   |   6