Question

In the equation, x is the mean of the frequency distribution and S is the standard deviation of the frequency distribution. Complete the table by calculating the z score.

X	f	X−x	z = (X−x) ÷ S
96	1
94	1
92	1
87	1
85	1
84	1
83	1
82	1
79	1
78	1
76	1
73	1
72	1
69	2
67	2
66	1
63	1
62	1
61	2
51	1
44	1
42	1

T scores = 10z + 50

Complete the table by calculating the T score.

(25 points)

Score	f (frequency)	T

Answer 1

First we find the mean(x) and the standard deviation(s)

X	f	f.X	x	(X-x)^2	f*((X-x)^2)
96	1	96	72.12	570.2544	570.2544
94	1	94	72.12	478.7344	478.7344
92	1	92	72.12	395.2144	395.2144
87	1	87	72.12	221.4144	221.4144
85	1	85	72.12	165.8944	165.8944
84	1	84	72.12	141.1344	141.1344
83	1	83	72.12	118.3744	118.3744
82	1	82	72.12	97.6144	97.6144
79	1	79	72.12	47.3344	47.3344
78	1	78	72.12	34.5744	34.5744
76	1	76	72.12	15.0544	15.0544
73	1	73	72.12	0.7744	0.7744
72	1	72	72.12	0.0144	0.0144
69	2	138	72.12	9.7344	19.4688
67	2	134	72.12	26.2144	52.4288
66	1	66	72.12	37.4544	37.4544
63	1	63	72.12	83.1744	83.1744
62	1	62	72.12	102.4144	102.4144
61	2	122	72.12	123.6544	247.3088
51	1	51	72.12	446.0544	446.0544
44	1	44	72.12	790.7344	790.7344
42	1	42	72.12	907.2144	907.2144

Mean is given by the formula :

x = 1803 / 25 = 72.12

Standard deviation is given by the formula :

Standard deviation on calculation , S = 14.39421

Next we compute the z score and t score which have been tabulated below:

X	f	X-x	z = (X-x)/S	T = 10z + 50
96	1	23.88	1.65900039	66.590004
94	1	21.88	1.52005563	65.200556
92	1	19.88	1.38111088	63.811109
87	1	14.88	1.03374899	60.33749
85	1	12.88	0.89480423	58.948042
84	1	11.88	0.82533185	58.253319
83	1	10.88	0.75585947	57.558595
82	1	9.88	0.6863871	56.863871
79	1	6.88	0.47796996	54.7797
78	1	5.88	0.40849758	54.084976
76	1	3.88	0.26955283	52.695528
73	1	0.88	0.06113569	50.611357
72	1	-0.12	-0.0083367	49.916633
69	2	-3.12	-0.2167538	47.832462
67	2	-5.12	-0.3556986	46.443014
66	1	-6.12	-0.425171	45.74829
63	1	-9.12	-0.6335881	43.664119
62	1	-10.12	-0.7030605	42.969395
61	2	-11.12	-0.7725328	42.274672
51	1	-21.12	-1.4672566	35.327434
44	1	-28.12	-1.9535633	30.464367
42	1	-30.12	-2.092508	29.07492