Question

4. Here are data: 9.04, 11.95, 5.58, 9.81, 7.33, 6.96, 7.24, 4.26, 10.84, 4.82, 5.68

For these data, present the following information (while you may use SPSS or other software to calculate the following, do not copy and paste SPSS or other software output except for i; instead report results you obtained by the letter identification below so I can quickly locate your response;

(a) Mean

(b) Median

(c) Mode

(d) Sample Variance

(e) Sample Standard Deviation

(f) Range

(g) What is the percentile rank for a score of 6.96 for these data?

(h) What is the z score for a score of 5.58?

(i) Ungrouped frequency display (include frequency, relative frequency, and cumulative relative frequency)

Answer 1

I used R software to solve this problem.

R codes:

> x=c(9.04, 11.95, 5.58, 9.81, 7.33, 6.96, 7.24, 4.26, 10.84, 4.82, 5.68)
> mean(x)
[1] 7.591818
> median(x)
[1] 7.24
> table(x)
x
4.26 4.82 5.58 5.68 6.96 7.24 7.33 9.04 9.81 10.84 11.95
1 1 1 1 1 1 1 1 1 1 1
> var(x)
[1] 6.363996
> sd(x)
[1] 2.522696
> range(x)
[1] 4.26 11.95

Answers Mean = 7.59.18 b) median = 7.24 Mode: There is no mode in data Mode is the most frequent value of the value corresponds to high frequency. But here al values have same frequency. Hence there is no modal vallie in data d) sample variance = 6.3640 e) sample standard deviation = 2.5227 & Range = Max - Min 11.95 - 4.26

1 percentile rank for x = 6.96 P ( X 26.96) = P(x-4 3 6.96- 7.59 2.52 - P(Z = -0.25) 0.4013 = percentile rank for score 6.96 is 40.13 Za X-4 - 0 5-58 - 7:59 2 .52 -0.7976 frequency Relative fregn Cunwative Rel free du Yu 3/11 2/11 1 1/ 3/ X 4.26 4.82 5.58 5-68 6.96 7.25 7.33 9.04 9.81 10.84 11.95 4/1 5/1 6111 1 7/1 1 8111 1/11 1/16 1/11 1/11 9/11 10/11
> length(x)
[1] 11