Chapter 1.3, Problem 2.1CYU

To determine

To Find: Five Number summary for the given data.

Answer to Problem 2.1CYU

1. The minimum: $307$
2. Q1: $311$
3. The median: $317.5$
4. Q3: $324$
5. The maximum: $353$

Explanation of Solution

Given information:

  $338,318,353,313,318,326,307,317,311,311$

Five number summaries basically gives rough data.

No. of observations: $10$

After arranging the given set of data in ascending order:

  $307,311,311,313,317,318,318,326,338,353$

First to find out the median arrange the data in ascending order and took middle values as a median.

So here median is $\frac{317+318}{2}=317.5$

Median: $317.5$

From the above arranged data it is observed that the maximum: $353$ and the minimum: $317$

Now, splits the list of two halves:

  $307,311,311,313,317$ and $318,318,326,338,353$

And since there are $5$ numbers in each halves, it is easy to find out the sub medians that is first and third quartiles.

So $Q_1=311$ and the minimum: $Q_2:326$

Five Number summaries for the given data consist of:

1. The minimum: $317$
2. $Q_1=311$
3. The median: $317.5$
4. $Q_3=326$
5. The maximum: $353$