# Median Worksheet

### Solutions

1Calculate the median for the following set of numbers: 5, 3, 6, 5, 4, 5, 2, 8, 6, 5, 4, 8, 3, 4, 5, 4, 8, 2, 5, 4.

2Find the median for the following set of numbers:

3, 5, 2, 6, 5, 9, 5, 2, 8, 6.

3Given the series:

3, 5, 2, 7, 6, 4, 9.

3, 5, 2, 7, 6, 4, 9, 1.

Calculate:

The median.

The quartiles 1 and 3.

The deciles 2 and 7.

The percentiles 32 and 85.

4Given the statistical distribution of the table.

 xi 61 64 67 70 73 fi 5 18 42 27 8

Calculate the median.

5A statistical distribution is given by the following table:

 [10, 15) [15, 20) [20, 25) [25, 30) [30, 35) fi 3 5 7 4 2

Calculate:

The median.

The quartiles 1 and 3.

The deciles 3 and 6.

The percentiles 30 and 70.

6Given the statistical distribution:

 [0, 5) [5, 10) [10, 15) [15, 20) [20, 25) [25, ∞) fi 3 5 7 8 2 6

Calculate:

The median.

The quartiles 2 and 3.

7Given the set:

10, 13, 4, 7, 8, 11 10, 16, 18, 12, 3, 6, 9, 9, 4, 13, 20, 7, 5, 10, 17, 10, 16, 14, 8, 18.

Find their median and quartiles.

8The heights of the players (in centimeters) from a basketball team are represented by the table:

 Height [170, 175) [175, 180) [180, 185) [185, 190) [190, 195) [195, 2.00) No. of players 1 3 4 8 5 2

Calculate:

1. The mean.

2. The median.

3. The standard deviation.

4. How many players are above the mean plus one standard deviation?

9The following graph is a histogram representing the weight of 100 children:

1. Create the respective table of distribution.

2. If John weighs 72 pounds, how many students are lighter than he is?

3. Calculate the median.

4. It what quartile are 25% of the heaviest pupils found?

10Given the absolute cumulative frequency table:

 Age Fi [0, 2) 4 [2, 4) 11 [4, 6) 24 [6, 8) 34 [8, 10) 40

Calculate the difference between the values that are the 10 central ages?

## 1

Calculate the median for the following set of numbers: 5, 3, 6, 5, 4, 5, 2, 8, 6, 5, 4, 8, 3, 4, 5, 4, 8, 2, 5, 4.

 xi fi Fi 2 2 2 3 2 4 4 5 9 5 6 15 6 2 17 8 3 20 20

20/2 = 10 Me = 5

## 2

Find the median for the following set of numbers:

3, 5, 2, 6, 5, 9, 5, 2, 8, 6.

2, 2, 3, 5, 5, 5, 6, 6, 8, 9.

10/2 = 5

## 3

Given the series:

3, 5, 2, 7, 6, 4, 9.

3, 5, 2, 7, 6, 4, 9, 1.

Calculate:

The median.

The quartiles 1 and 3.

The deciles 2 and 7.

The percentiles 32 and 85.

3, 5, 2, 7, 6, 4, 9.

2, 3, 4, 5, 6, 7, 9.

Me = 5

r = 9 − 2 = 7

#### Deciles

7 · (2/10) = 1.4 D2 = 3

7 · (7/10) = 4.9 D7 = 6

#### Percentiles

7 · (32/100) = 2,2 P32 = 4

7 · (85/100) = 5.9 P85 = 7

3, 5, 2, 7, 6, 4, 9, 1.

r = 9 - 1 = 8

#### Deciles

8 · (2/10) = 1.6 D2 = 2

8 · (7/10) = 5.6 D7 = 6

#### Percentiles

8 · (32/100) = 2.56 P32 = 3

8 · (85/100) = 6.8 P85 = 7

## 4

Given the statistical distribution of the table.

 xi 61 64 67 70 73 fi 5 18 42 27 8

Calculate the median.

 xi fi Fi 61 5 5 64 18 23 67 42 65 71 27 92 73 8 100 100

#### Median

102/2 = 50 Me = 67

## 5

A statistical distribution is given by the following table:

 [10, 15) [15, 20) [20, 25) [25, 30) [30, 35) fi 3 5 7 4 2

Calculate:

The median.

The quartiles 1 and 3.

The deciles 3 and 6.

The percentiles 30 and 70.

 xi fi Fi [10, 15) 12.5 3 3 [15, 20) 17.5 5 8 [20, 25) 22.5 7 15 [25, 30) 27.5 4 19 [30, 35) 32.5 2 21 21

## 6

Given the statistical distribution:

 [0, 5) [5, 10) [10, 15) [15, 20) [20, 25) [25, ∞) fi 3 5 7 8 2 6

Calculate:

The median.

The quartiles 2 and 3.

 xi fi Fi [0, 5) 2.5 3 3 [5, 10) 7.5 5 8 [10, 15) 12.5 7 15 [15, 20) 17.5 8 23 [20, 25) 22.5 2 25 [25, ∞) 6 31 31

## 7

Given the set:

10, 13, 4, 7, 8, 11 10, 16, 18, 12, 3, 6, 9, 9, 4, 13, 20, 7, 5, 10, 17, 10, 16, 14, 8, 18

Find their median and quartiles.

First arrange the data from smallest to largest:

3, 4, 4, 5, 6, 7, 7, 8, 8, 9, 9, 10, 10, 10, 10, 11, 12, 13, 13, 14, 16, 16, 17, 18, 18, 20

#### Median

26/2 = 13.

As the number of data is even, the median is the average of the two central punctuations:

#### Quartiles

26/4 = 6.5 Q1 = 7

Q2 = Me = 10

(26 · 3)/4 = 19.5 Q3 = 14

## 8

The heights of the players (in centimeters) from a basketball team are represented by the table:

 Height [170, 175) [175, 180) [180, 185) [185, 190) [190, 195) [195, 2.00) No. of players 1 3 4 8 5 2

Calculate:

1. The mean.

2. The median.

3. The standard deviation.

4. How many players are above the mean plus one standard deviation?

 xi fi Fi xi · fi xi2 · fi [1.70, 1.75) 1.725 1 1 1.725 2.976 [1.75, 1.80) 1.775 3 4 5.325 9.453 [1.80, 1.85) 1.825 4 8 7.3 13.324 [1.85, 1.90) 1.875 8 16 15 28.128 [1.90, 1.95) 1.925 5 21 9.625 18.53 [1.95, 2.00) 1.975 2 23 3.95 7.802 23 42.925 80.213

#### 4

x + σ = 1.866+ 0.077 = 1.943

This value belongs to a percentile that is in the penultimate interval.

There are only 3 players above x + σ.

## 9

The following graph is a histogram representing the weight of 100 children:

1. Create the respective table of distribution.

2. If John weighs 72 pounds, how many students are lighter than he is?

3. Calculate the mode.

4. Calculate the median.

5. It what quartile are 25% of the heaviest pupils found?

#### 1

 xi fi Fi [60,63) 61.5 5 5 [63, 66) 64.5 18 23 [66, 69) 67.5 42 65 [69, 72) 70.5 27 92 [72, 75) 73.5 8 100 100

#### 2

5 + 18 + 42 + 27 = 92 students lighter than John.

#### 4

25% of the heaviest students are found in the third quartile.

## 10

Given the absolute cumulative frequency table:

 Edad Fi [0, 2) 4 [2, 4) 11 [4, 6) 24 [6, 8) 34 [8, 10) 40

Calculate the difference between the values that are the 10 central ages?

 xi fi Fi [0, 2) 1 4 4 [2, 4) 3 7 11 [4, 6) 5 13 24 [6, 8) 7 10 34 [8, 10) 9 6 40 40

The 10 students represent 25% of the central distribution.

Find: P37.5 y P62.5.

The 10 central ages are in the interval: [4.61, 6.2] .