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:

Histogram

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  

Median

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.

Median

10/2 = 5 Statistical Median


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

Quartiles

Quartiles Example

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.

Median

Median Exercise

r = 9 - 1 = 8

Quartiles

Quartiles Solution

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  

Median

Median Solution

Quartiles

Quartile Example

Quartile Example

Deciles

Decile Exercise

Decile Exercise

Percentiles

Percentile Calculations

Percentile Calculations


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  

Median

Median Problem

Quartiles

Quartile Problem

Quartile Problem


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:

Median Calculations

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

Mean

Mean

Median

Median

Standard Deviation

Standard Deviation

4

x + σ = 1.866+ 0.077 = 1.943

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

formulas

formulas

There are only 3 players above x + σ.


9

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

Histogram

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.

Median

Median

4

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

Median


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  

formulas

The 10 students represent 25% of the central distribution.

Central Distribution Diagram

Find: P37.5 y P62.5.

formulas

formulas

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