Question

7. The following frequency distribution table represents a survey of 100 resort dlub managers on their annual salaries. Find the midpoint, relative frequency, cumulative frequency, mean, standard deviation and variance for the frequency distribution table, then graph the histogram of the data. ay Managers) ($1000s) 15-25 26-36 15 4353172a 111757 S 48-58 uj 59-69 751750 slo abolo ak loo 10% 94 gb 5% 30119 3630 5Wg/616%|loo 70-80 81-91 6 total 1100 Su5som bone tion w many 3-Persm Committeescan be Seluctedd from Jo emplyes 4) Evaluate 0 lkC7

Answer 1

Midpoint: (Upper class limit + Lower class limit)/2

For Example:

First Class: (25 + 15)/2 = 40/2 = 20

Second class: (36+26)/2 = 62/2 = 31

Simillarly Find out for others............

Relative Frequency: Frequency/sample size (N)

For First class: 8/100 = 0.08

For second class: 15/100 = 0.15

And so on .....

Mean:

$Mean = \frac{\sum Fi*Xi}{Total Frequency} = \frac{5091}{100} = 50.91$

Standard deviation:

$SD = \sqrt{\frac{1}{N} * \sum Fi(Xi-\bar{X})^2} = \sqrt{\frac{1}{100} * 31386.19} = 17.72$

Variance:

$VAR = \frac{1}{N} * \sum Fi(Xi-\bar{X})^2 = \frac{1}{100} * 31386.19 = 313.86$

Table:

CI	Frequency	Xi	Xi * Fi	(Xi - $\bar{X}$)	(Xi-$\bar{X}$)2	Fi*(Xi-$\bar{X}$)2	Rel. Freq	Cumm. Freq.
15 - 25	8	20	160	-30.91	955.43	7643.42	0.08	100
26 - 36	15	31	465	-19.91	396.41	5946.12	0.15	92
37 - 47	20	42	840	-8.91	79.39	1587.76	0.2	77
48 - 58	24	53	1272	2.09	4.37	104.83	0.24	57
59 - 69	17	64	1088	13.09	171.35	2912.92	0.17	33
70 - 80	10	75	750	24.09	580.33	5803.28	0.1	16
81 - 91	6	86	516	35.09	1231.31	7387.85	0.06	6
Total	100	371	5091			31386.19

Histogram Of the Data:

Histogram 30 25 20 15 10 15-25 26-36 37-4748-58 59-69 70-80 81-91 Annual salary ($1000s)