Answer 3 Easy questions for the data below (50 Income data points in ascending o

Question

Answer 3 Easy questions for the data below (50 Income data points in ascending order already)

(a) Use the percentile location formula, and the three associated rules (1 mark) to determine: 70th Percentile (DONT USE EXCEL- I want to see working)

(b) Briefly explain what the 70th percentile that you have determined informs you about the Income variable

(c) Determine the Inter-Quartile Range of “Income” variable and provide a brief explanation of what information this statistic provides about your sample data.

V1 45,000 45,000 48,652 58 70,0 95,297 S 95,297 $ 95,297 595,570 95,818 96,210 96,286 596,691 97,176 $97,864 98,191 98,364

Explanation / Answer

Order all the values in the data set from smallest to largest.

Multiply k percent by the total number of values, n.

This number is called the index.

If the index obtained in Step 2 is not a whole number, round it up to the nearest whole number and go to Step 4a. If the index obtained in Step 2 is a whole number, go to Step 4b.

4a.Count the values in your data set from left to right (from the smallest to the largest value) until you reach the number indicated by Step 3.

The corresponding value in your data set is the kth percentile.

4b.Count the values in your data set from left to right until you reach the number indicated by Step 2.

The kth percentile is the average of that corresponding value in your data set and the value that directly follows it.

a) 70th percentile= 0.70*49

= 34.3

Rounding up to the nearest whole number, you get 34.

So After arranging the dataset in ascending order the 34th value is 99398.

So, 70th percentile = 99398

c) For Inter-Quartile Range,

25th percentile= 0.25*49 = 12.25 =12

So After arranging the dataset in ascending order the 12th value is 95297.

So,25th percentile = 95297

75th percentile= 0.75*49 = 36.75 =37

So After arranging the dataset in ascending order the 37th value is 100200

So,75th percentile = 100200

The interquartile range equation is IQR = Q3 – Q1.

= 100200-95297

= 4903

The Interquartile Range Calculator enables you to enter a series of numbers and get the interquartile range without having to solve the interquartile range equation. The interquartile range is the difference between the third quartile and the first quartile in a data set, giving the middle 50%.

The IQR is often seen as a better measure of spread than the range as it is not affected by outliers.

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