Math, asked by swasti2654, 7 months ago

for the data given below, calculate the mean,mode and median 5,8,9,6,9,4,3,3,9,6,3,9,7,3,4,5,9
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Answers

Answered by gpandu1111
1

Unit 5 Section 2 : Mean, Median, Mode and Range

The mean, median and mode are types of average.

The range gives a measure of the spread of a set of data.

This section revises how to calculate these measures for a simple set of data.

It then goes on to look at how the measures can be calculated for a table of data.

Calculating the Mean, Median, Mode and Range for simple data

The table below shows how to calculate the mean, median, mode and range for two sets of data.

Set A contains the numbers 2, 2, 3, 5, 5, 7, 8 and Set B contains the numbers 2, 3, 3, 4, 6, 7.

MeasureSet A

2, 2, 3, 5, 5, 7, 8Set B

2, 3, 3, 4, 6, 7The Mean

To find the mean, you

need to add up all the

data, and then divide

this total by the number

of values in the data.

Adding the numbers up gives:

2 + 2 + 3 + 5 + 5 + 7 + 8 = 32

There are 7 values, so you divide

the total by 7:    32 ÷ 7 = 4.57...

So the mean is 4.57 (2 d.p.)

Adding the numbers up gives:

2 + 3 + 3 + 4 + 6 + 7 = 25

There are 6 values, so you divide

the total by 6:    25 ÷ 6 = 4.166...

So the mean is 4.17 (2 d.p.)

The Median

To find the median, you

need to put the values

in order, then find the

middle value. If there are

two values in the middle

then you find the mean

of these two values.

The numbers in order:

2 , 2 , 3 , (5) , 5 , 7 , 8

The middle value is marked in

brackets, and it is 5.

So the median is 5

The numbers in order:

2 , 3 , (3 , 4) , 6 , 7

This time there are two values in

the middle. They have been put

in brackets. The median is found

by calculating the mean of these

two values:    (3 + 4) ÷ 2 = 3.5

So the median is 3.5

The Mode

The mode is the value

which appears the most

often in the data. It is

possible to have more

than one mode if there

is more than one value

which appears the most.The data values:

2 , 2 , 3 , 5 , 5 , 7 , 8

The values which appear most

often are 2 and 5. They both

appear more time than any

of the other data values.

So the modes are 2 and 5

The data values:

2 , 3 , 3 , 4 , 6 , 7

This time there is only one value

which appears most often - the 

number 3. It appears more times

than any of the other data values.

So the mode is 3

The Range

To find the range, you

first need to find the

lowest and highest values

in the data. The range is

found by subtracting the

lowest value from the

highest value.The data values:

2 , 2 , 3 , 5 , 5 , 7 , 8

The lowest value is 2 and the

highest value is 8. Subtracting

the lowest from the highest

gives:    8 - 2 = 6

So the range is 6

The data values:

2 , 3 , 3 , 4 , 6 , 7

The lowest value is 2 and the

highest value is 7. Subtracting

the lowest from the highest

gives:    7 - 2 = 5

So the range is 5

Practice Question (for simple data)

Work out the mean, median, mode and range for the simple data set below,

then click on the button marked  to see whether you are correct.

A data set contains these 12 values: 3, 5, 9, 4, 5, 11, 10, 5, 7, 7, 8, 10

(a) What is the mean?

(b) What is the median?

(c) What is the mode?

(d) What is the range?

Answered by ItzUltraParthStar
1

Calculate Mean, Median and Mode for the following data. Which of these three measures if minimum?

Marks s(out of 15) 7 4 10 9 15 12 7 9 9

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ANSWER

Arranging given marks in ascending order,

4,7,7,9,9,9,10,12,15

Number of observations (n)=9

⇒ Mean=

9

4+7+7+9+9+9+10+12+15

=

9

82

=9.11

⇒ Here, number 9 occurs maximum number of times i.e 3 times.

∴ Mode=9

Number of observation is odd number

∴ Median=(

2

n+1

)

th

obs=(

2

9+1

)

th

obs=5

th

obs

Here, 5

th

obs=9

∴ Median=9

⇒ So, we can see mean measure is maximum and mode,median measures are minimum.

Step-by-step explanation:

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