Find the 5 number summary for the data shown below.

Question

Find the 5 number summary for the data shown below.

46	7
41	54
79	4
37	6
93	58

5 number summary:

, , , , 

Answer 1

Hi Tra'von,

Five-Number Summary means minimum, first quartile, median, third quartile, and maximum. First step is to list all values in numerical order from smallest to largest. So:

4,6,7,37,41,46,54,58,79,93

Minimum is 4. That's your first number. First quartile equates to 25th percentile, so take:

0.25*n, where n is total sample size

n=10

0.25*n=2.5

Now, you want the value at position 2.5, which technically doesn't exist, so we take the average of the values at positions 2 and 3, which is:

(6+7)/2=6.5

That's the first quartile. Now, the median is the value directly in the middle. In a ten-point set, this is the value between positions 5 and 6. Again, we take the average of those two positions:

(41+46)/2=43.5

That's the median. Now, formula for the third quartile is similar to that for first quartile. Third quartile equates to 75th percentile, so:

0.75*n; n=sample size=10

0.75*n=7.5

Again, we now take the average of positions 7 and 8:

(54+58)/2=56

That's the third quartile. The maximum is simply the highest value in the dataset, 93.

Five Number Summary: 4, 6.5, 43.5, 56, 93

I hope this helps.