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Answer:
q. surnames were randomly picked up form a local telefone directly and the frequncey distribution of the number of letters in the English alfabets in. the. surnames. was. recorded.a.follow.....if
mean. of. data. 6.6...find. missing. x. and. y...
Step-by-step explanation:
100 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in the English alphabets in the surnames was obtained as follows:
Number of letters
1−4
4−7
7−10
10−13
13−16
16−19
Number of surnames
6
30
40
16
4
4
Determine the median number of letters in the surnames. Find the mean number of letters in the surnames? Also, find the modal size of the surnames.
Medium
Video Explanation
Solution To Question ID 465498
ANSWER
Let us prepare the following table to compute the median :
Number of letters Number of surnames (Frequency) Cumulative frequency
1−4 6 6
4−7 30 36
7−10 40 76
10−13 16 92
13−16 4 96
16−19 4 100=n
We have, n=100
⇒
2
n
=50
The cumulative frequency just greater than
2
n
is 76 and the corresponding class is 7–10.
Thus, 7–10 is the median class such that
2
n
=50,l=7,f=40,cf=36 and h=3
Substitute these values in the formula
Median, M=l+
⎝
⎛
f
2
n
−cf
⎠
⎞
×h
M=7+(
40
50−36
)×3
M=7+
40
14
×3=7+1.05=8.05
Now, calculation of mean:
Number of letters Mid-Point (x
i
) Frequency (f
i
) f
i
x
i
1−4 2.5 6 15
4−7 5.5 30 165
7−10 8.5 40 340
10−13 11.5 16 184
13−16 14.5 4 58
16−19 17.5 4 70
Total 100 832
Therefore, Mean,
x
ˉ
=
∑f
i
∑f
i
x
i
=
100
832
=8.32
Calculation ofMode:
The class 7–10 has the maximum frequency therefore, this is the modal class.
Here,
l=7,h=3,f
1
=40,f
0
=30 and f
2
=16
Now, let us substitute these values in the formula
Mode =l+(
2f
1
−f
0
−f
2
f
1
−f
0
)×h
=7+
80−30−16
40−30
×3
=7+
34
10
×3=7+0.88=7.88
Hence, median =8.05, mean =8.32 and mode =7.88