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DESCRIPTIVE STATISTICS CASE STUDY:
The four variables shown in the data set below are set up to represent a fictitious
study of gender, weight and fitness score. The variables include gender, ranking, weight
and score. In this example, gender is coded as m or f (recoded as 1 or 2 for
computations), weight is the participant's weight, score is a value that the participant
scored in a fitness test and rank is their ranking based on that score.
Gender Ranking Weight Score
m 1 200 95
m 2 110 92
f 3 103 91
f 4 145 90
f 5 130 88
m 6 180 82
m 7 170 80
f 8 90 75
f 9 102 70
m 10 225 60
m 11 225 59
m 12 108 55
f 13 108 55
m 14 108 55
m 15 167 50
EACH OF THE VARIABLES IS EXAMINED IN THE CHART BELOW:
Statistics
GENDER RANKING SCORE WEIGHT
N Valid
Missing
Statistic
Statistic
15
0
15
0
15
0
15
0
Mean Statistic
St. Error
1.40
.13
8.0000
1.1547
73.1333
4.1928
144.7333
12.0224
Median Statistic 1.00 8.0000 75.0000 130.0000
Mode Statistic 1 1.00 a 55.00 108.00
Std. Deviation Statistic .51 4.4721 16.2387 46.5625
Variance Statistic .26 20.0000 263.6952 2168.0667
Skewness Statistic
St. Error
.455
.580
.000
.580
-.065
.580
.625
.580
Kurtosis Statistic
St. Error
-2.094
1.121
-1.200
1.121
-1.753
1.121
-1.037
1.121
Range Statistic 1 14.00 45.00 135.00
Minimum Statistic 1 1.00 50.00 90.00
Maximum Statistic 2 15.00 95.00 225.00
a. Multiple modes exist. The smallest value is shown
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YOUR TURN Using the values from the GENDER variable in table above, answer the
following questions.
===============================================================
1. What type of data does gender represent?
2. What does the mean gender of 1.40 tell us?
3. What would be the appropriate measure of central tendency for GENDER?
4. What is the value for central tendency?
===============================================================
YOUR TURN Using the values from the RANKING variable in table above, answer the
following questions.
5. What type of data does RANKING represent?
6. What is the appropriate measure of central tendency?
7. What is the value for central tendency?
8. Would it be appropriate to describe the average ranking? Why or why not?
===============================================================
YOUR TURN Using the values from the SCORE variable in the table above, answer the
following questions.
9. What type of data does SCORE represent?
10. What is the mean, median and mode of this data set?
11. What does the difference between the mean, median and mode tell you?
12. Is this data set skewed? If so, in which direction?
13. What is the range of the data set? How is this determined?
14. What does the kurtosis figure tell you?
15. Do you think this data is normally distributed? Why?
16. What does the standard error tell you?
17. What is the relationship between the variance and the standard deviation? What do
these numbers tell you?
===============================================================
YOUR TURN Using the values from the WEIGHT variable in the table above, answer
the following questions.
===============================================================
18. What type of data does WEIGHT represent?
19. What is the mean, median and mode of this data set?
20. What does the difference between the mean, median and mode tell you?
21. Is this data set skewed? If so, in which direction?
22. What is the range of the data set? How is this determined?
23. What does the kurtosis figure tell you?
24. Do you think this data is normally distributed? Why?
25. What does the standard error tell you?
26. What is the relationship between the variance and the standard deviation? What do
these numbers tell you?

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1)  Gender xxxxxxx Nominal type xxxxxxx data.

2) Total xxxxxxx xxxxxxx males=9

Total xxxxxxx of females=6

Male xxxxxxx as 1

Female xxxxxxx as xxxxxxx xxxxxxx height="36" src="file:///C:/Users/ANKITA/AppData/Local/Temp/msohtmlclip1/01/clip_image002.gif" xxxxxxx />

            =

            xxxxxxx a nominal xxxxxxx xxxxxxx data, xxxxxxx does not xxxxxxx us anything.

3) xxxxxxx appropriate xxxxxxx xxxxxxx central tendency xxxxxxx GENDER would xxxxxxx ‘Mode’

4) Mode xxxxxxx the most xxxxxxx appearing data xxxxxxx the set. xxxxxxx xxxxxxx central xxxxxxx is the xxxxxxx that is xxxxxxx to xxxxxxx xxxxxxx of Male) xxxxxxx male appears xxxxxxx most number xxxxxxx times.

5) RANKING xxxxxxx Ordinal type xxxxxxx data.

6) The xxxxxxx xxxxxxx of xxxxxxx tendency is xxxxxxx Value for xxxxxxx tendency=median=8.0000

8) xxxxxxx xxxxxxx not appropriate xxxxxxx describe the xxxxxxx ranking because xxxxxxx is Ordinal xxxxxxx of data xxxxxxx it is xxxxxxx xxxxxxx Moreover xxxxxxx does not xxxxxxx how much xxxxxxx one xxxxxxx xxxxxxx from the xxxxxxx participant.

9) SCORE xxxxxxx Ratio type xxxxxxx data.

10) For xxxxxxx 73.1333

Median= 75.0000

Mode= xxxxxxx (Since multiple xxxxxxx xxxxxxx we xxxxxxx showing the xxxxxxx value)

11) Mean xxxxxxx us xxxxxxx xxxxxxx score of xxxxxxx participants. Median xxxxxxx us the xxxxxxx of the xxxxxxx in middle xxxxxxx sorted according xxxxxxx xxxxxxx scores. xxxxxxx tells us xxxxxxx score with xxxxxxx most xxxxxxx xxxxxxx participants. Mean xxxxxxx the better xxxxxxx over here xxxxxxx by median xxxxxxx is almost xxxxxxx to the xxxxxxx xxxxxxx mode xxxxxxx the worst xxxxxxx in scores xxxxxxx type xxxxxxx xxxxxxx The difference xxxxxxx the values xxxxxxx mean, median xxxxxxx mode tells xxxxxxx data is xxxxxxx normally distributed xxxxxxx xxxxxxx skewed.

12) xxxxxxx is a xxxxxxx data set xxxxxxx it xxxxxxx xxxxxxx to the xxxxxxx since Mode<Mean xxxxxxx Mode< Median.

13) xxxxxxx of the xxxxxxx set is xxxxxxx It is xxxxxxx xxxxxxx Maximum xxxxxxx Score.

14) Kurtosis xxxxxxx tells that xxxxxxx distribution xxxxxxx xxxxxxx is flatter xxxxxxx a normal xxxxxxx The data xxxxxxx not normally xxxxxxx because in xxxxxxx of normal xxxxxxx xxxxxxx Standard xxxxxxx tells the xxxxxxx by which xxxxxxx obtained xxxxxxx xxxxxxx differ from xxxxxxx actual value. xxxxxxx obtained mean xxxxxxx deviate from xxxxxxx actual value xxxxxxx  where xxxxxxx height="23" src="file:///C:/Users/ANKITA/AppData/Local/Temp/msohtmlclip1/01/clip_image010.gif" xxxxxxx />= standard xxxxxxx n=number xxxxxxx xxxxxxx Standard error xxxxxxx mean for xxxxxxx is. xxxxxxx may deviate xxxxxxx  =

18) xxxxxxx represents xxxxxxx xxxxxxx of data.

19) xxxxxxx Weight,

Mean= 144.7333

Median= xxxxxxx 108

20) Mean xxxxxxx showing more xxxxxxx estimation and xxxxxxx of data xxxxxxx xxxxxxx deviates xxxxxxx the mean xxxxxxx a notable xxxxxxx hence xxxxxxx xxxxxxx be considered xxxxxxx better option xxxxxxx measure the xxxxxxx tendency than xxxxxxx Mode is xxxxxxx less than xxxxxxx xxxxxxx thus xxxxxxx be used xxxxxxx measure the xxxxxxx tendency xxxxxxx xxxxxxx data. The xxxxxxx in the xxxxxxx of mean, xxxxxxx and mode xxxxxxx that data xxxxxxx not normally xxxxxxx xxxxxxx are xxxxxxx It is xxxxxxx skewed data xxxxxxx and xxxxxxx xxxxxxx skewed to xxxxxxx right since xxxxxxx and Mode< xxxxxxx Range of xxxxxxx data set xxxxxxx 135.00. It xxxxxxx xxxxxxx by xxxxxxx Weight-Minimum Weight.

23) xxxxxxx figure tells xxxxxxx since xxxxxxx xxxxxxx is negative, xxxxxxx distribution of xxxxxxx is flatter xxxxxxx a normal xxxxxxx The data xxxxxxx not normally xxxxxxx xxxxxxx in xxxxxxx of normal xxxxxxx mean=mode=median.

25) Standard xxxxxxx tells xxxxxxx xxxxxxx by which xxxxxxx obtained value xxxxxxx differ from xxxxxxx actual value. xxxxxxx obtained mean xxxxxxx deviate from xxxxxxx xxxxxxx value xxxxxxx  where xxxxxxx height="23" xxxxxxx xxxxxxx />= standard xxxxxxx n=number of xxxxxxx Standard error xxxxxxx mean for xxxxxxx is. xxxxxxx xxxxxxx deviate xxxxxxx  =

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