Question

Singees the hergh ts Cin inches) of 130 member S of a choir. full chair: The frequency table shows a)Find the median and IQR. Height Count Height Count b) Find the mean and 69 60 61 Standard deviation 31 c) Display these data with histogram 5 ㅋ3 74 4 64 ao 18 75 4 a few describing the distribution. d)write sentences 구6 1 a 83885835

Answer 1

a)

Solution: * Frequency o (1) fox (3) = (2) (1) (5) 120 366 558 441 320 1300 1188 469 816 for? = (f - x) * (x) (4) = (3) x (1) 7200 22326 34596 27783 20480 84500 78408 31423 55488 23805 53900 40328 46656 21316 10952 22500 5776 345 770 568 648 292 148 300 76 --- n = 130 Ef-x=8725 {f.x2 = 587437

Median :
M = value of (n/2)th observation

= value of (130/2)th observation

= value of 65th observation

From the column of cumulative frequency cf, we find that the 65th observation is 66.

Hence, the median of the data is 66.

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Q1=(n+1)/4 th value of the observation

=(131/4)th value of the observation

=(32.75)th value of the observation

=65

Q3=3(n+1)/4 th value of the observation

=(3*131/4)th value of the observation

=(98.25)th value of the observation

=70

IQR = Q3 - Q1 = 70 - 65 = 5

b)

Mean ˉx=∑fx/n

=8725/130

=67.1154

Σ.χ. (ΣΣ): Sample Standard deviation S = V- η - 1 527437 (125 129 13 = 587437 - 585581.7308 129 1855.2692 129 = 14.3819 = 3.7924

c)

Histogram frequency 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 height

d)

data is roughly symmeteric .

height 66 and 65 inches has maximum frequency.