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Question 5 (5 points) Consider the histogram below for the heights of students in centimeters). Describe the center, shape, variation, and presence of outliers for the distribution. What is the class width being used here? Height of students 9 8 7 6 Frequency 4 3 2 1 0 Height (cm)

Answer 1

5) From the histogram we have,

Class	Frequency	X	Xf	(X-xbar)^2 f	Cf
114-115	1	114.5	114.5	98.01	1
115-116	1	115.5	115.5	79.21	2
116-117	1	116.5	116.5	62.41	3
117-118	1	117.5	117.5	47.61	4
118-119	2	118.5	237	69.62	6
119-120	2	119.5	239	48.02	8
120-121	2	120.5	241	30.42	10
121-122	3	121.5	364.5	25.23	13
122-123	3	122.5	367.5	10.83	16
123-124	4	123.5	494	3.24	20
124-125	4	124.5	498	0.04	24
125-126	5	125.5	627.5	6.05	29
126-127	6	126.5	759	26.46	35
127-128	8	127.5	1020	76.88	43
128-129	5	128.5	642.5	84.05	48
129-130	3	129.5	388.5	78.03	51
Total	51		6342.5	746.11

Center,

Mean

= ΣΧf Σ.f 6342.5/51 = 124.4

Mode is in the class 127 - 128

Median is = (52/2) th data =  26th data = Median is in the class (125-126)

Shape,

The distribution is negatively skewed. i.e. left skewed.

Variation,

Variance,

$\small =\frac{\sum( X-\bar{x})^{2}f}{\sum f-1}= 746.11/50 = 14.92$

Coefficient of variation,

$\small =\frac{S}{\bar{x}}*100\% = (\frac{\sqrt{14.92}}{124.4})*100\% = 3.11 \%$

There is no outlier in the distribution,

Class width = 1

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