Question

Question 8 (1 point) Following is a sample of the number of words spoken in each inauguration address for U.5. presidents. 1,125 2,978 1,172 1,507 4,776 3,801 2,015 2,463 4388 135 3,967 1,639 1,437 3,217 1.340 2 308 1681 2546 2158 2.170 5.433 698 What is the 32nd percentile? Wnte only a number as your answer

Answer 1

Answer

Required Solution :

Given Data =   We are given that the sample of number of words spoken in each inauguration address for U.S.Presidents.

We have to find 32^nd percentile for given sample. To find percentile , we use following formula :

     $P_{k}=Value\: \: of\: \: \frac{k\times (n+1)}{100} \: \: observation$

where k = 32 , n = number of observations = 23

First we need to sort the given sample in ascending order.

Sr. | Sample

No.| observations

1   135
2   698
3   1125
4   1172
5   1340
6   1437

7   1507

8   1615

9   1681
10   1729
11   2015
12   2158
13   2170
14   2308
15   2463
16   2546
17   2978
18   3217
19   3801
20   3967
21   4388
22   4776
23   5433

Thus 32nd percentile is :

$P_{32}=Value\: \: of\: \: \frac{32\times (23+1)}{100} \: \: observation$

$P_{32}=Value\: \: of\: \: \frac{32\times 24}{100} \: \: observation$

$P_{32}=Value\: \: of\: \: \frac{768}{100} \: \: observation$

$P_{32}=Value\: \: of\: \: 7.68^{th} \: \: observation$

$P_{32}=Value\: \: of\: \: 7^{th} \: \: observation + 0.68\times (8^{th}-7^{th})observation$

( 7^th observation = 1507   and 8^th observation = 1615 )

$P_{32}=1507 + 0.68\times (1615-1507)$

$P_{32}=1507 + 0.68\times 108$

$P_{32}=1507 + 73.44$

$P_{32}=1580.44$

Thus 32^nd percentile of given sample is $P_{32}=1580.44$ .