## What is the five number summary for this data set?

A five-number summary is especially useful in descriptive analyses or during the preliminary investigation of a large data set. A summary consists of five values: the most extreme values in the data set (the maximum and minimum values), the lower and upper quartiles, and the median.

## How do you explain quartiles?

The quartile measures the spread of values above and below the mean by dividing the distribution into four groups. A quartile divides data into three points—a lower quartile, median, and upper quartile—to form four groups of the dataset.

## How do you find the upper and lower quartiles?

1. The values in ascending order are: Median = (12th + first) ÷ 2.
2. Range = difference between the highest and lowest values. = 57 – 1.
3. Lower quartile = value of middle of first half of data Q1 = the median of 1, 11, 15, 19, 20, 24.
4. Upper quartile = value of middle of second half of data Q3
5. Interquartile range = Q3–Q1

## What is the formula to find quartiles?

First Quartile(Q1)=((n+1)/4)th Term also known as the lower quartile. The second quartile or the 50th percentile or the Median is given as: Second Quartile(Q2)=((n+1)/2)th Term. The third Quartile of the 75th Percentile (Q3) is given as: Third Quartile(Q3)=(3(n+1)/4)th Term also known as the upper quartile.

## How do you calculate quartiles?

Interquartile range – Higher To find the median value, or the value that is half way along the list, the method is to count the number of numbers, add one and divide by 2. To find the lower quartile or the value that is one quarter of the way along the list, count how many numbers there are, add 1 and divide by 4.

## What is Q1 Q2 Q3 in statistics?

Statistics Dictionary Q1 is the “middle” value in the first half of the rank-ordered data set. Q2 is the median value in the set. Q3 is the “middle” value in the second half of the rank-ordered data set.

## How do you find the lower quartile with odd numbers?

1. Use the median to divide the ordered data set into two-halves. If there is an odd number of data points in the original ordered data set, do not include the median (the central value in the ordered list) in either half.
2. The lower quartile value is the median of the lower half of the data.

## How do you find Q1 and Q3 in quartile deviation?

Calculation of quartile deviation can be done as follows,

1. Q1 is an average of 2nd, which is11 and adds the difference between 3rd & 4th and 0.5, which is (12-11)*0.5 = 11.50.
2. Q3 is the 7th term and product of 0.5, and the difference between the 8th and 7th term, which is (18-16)*0.5, and the result is 16 + 1 = 17.

## Do you count the median when finding quartiles?

Use the median to divide the ordered data set into two halves. Do not include the median into the halves. The lower quartile value is the median of the lower half of the data. The upper quartile value is the median of the upper half of the data.

## Can the first quartile equal the median?

A median divides a data set into two equal parts. Data can be described as being “above” or “below” the first quartile, but data is never “in” the first quartile. Q1: The first quartile is the middle (the median) of the lower half of the data set.

## How do you find the median and quartiles?

It is the distance between the upper and lower quartiles. To find the quartiles and median, put the numbers in order from smallest to largest. Then if there are an odd number of numbers in the list the median can be found by counting in from either end of the list to the (n + 1)/2nd number. This will be the median.