The modal mark is the mark which appeared the most. Observe the leaf in each of the stems to determine which number appeared the most.

5 appeared 3 times in the stem 4 more than the rest. The mark is obtained by joining the leaf to the stem.

The modal mark = Stem 4 and leaf 5 hence 45

The leaf represents each mark. Hence count how many leaves to determine the number of students who took the test.

Total number of students who took the test = 5 + 3 + 4 + 4 + 3 + 2
Total number of students who took the test = 21

The median is the middle number. The median mark is the middle mark. Locate the middle leaf and join its stem with the leaf to obtain the median mark.

The middle leaf is 5 (the 11th position) at stem 4, hence the median mark is 45

Write the numbers in ascending order from the stem and leaf by joining the stem and each of the leaves. Thus 4|0 = 40, 4|5 = 45, 4|7 = 47, 4|9 = 49, 5|1 = 51, 5|3 = 53 etc.

40,45,47,47,51,53,54,55,57,58,60,62,63,64,64,64,64,65,66,68,71,72,73,74,75,78,78,79,82,83,85,86,89,94,95

Now count the numbers. You can as well count the leaves to know how many items are in the plot

When you count, you will get 35

Write the numbers in ascending order from the stem and leaf by joining the stem and each of the leaves. Thus 4|0 = 40, 4|5 = 45, 4|7 = 47, 4|9 = 49, 5|1 = 51, 5|3 = 53 etc.

40,45,47,47,51,53,54,55,57,58,60,62,63,64,64,64,64,65,66,68,71,72,73,74,75,78,78,79,82,83,85,86,89,94,95

The median is the middle number of a set of data.

From the data, 65 is the middle weight

Write the numbers in ascending order from the stem and leaf by joining the stem and each of the leaves. Thus 4|0 = 40, 4|5 = 45, 4|7 = 47, 4|9 = 49, 5|1 = 51, 5|3 = 53 etc.

40,45,47,47,51,53,54,55,57,58,60,62,63,64,64,64,64,65,66,68,71,72,73,74,75,78,78,79,82,83,85,86,89,94,95

The mode/modal is the number that occurs the most in a set of data.

From the weights, 64 occurs the most

Median is the middle number or the average of the middle numbers when two numbers happen to be in the middle of an ordered numbers.

12 and x happens to be in the middle and so the median is the average (the sum of the numbers divided by 2) of 12 and x

The median is therefore calculated as:

Now calculate for the value of x

Every number is being divided by 1

We can therefore write the above equation as:

You can cross multiply to solve for the value of x

1 x (12+x) = 14 x 2

12 + x = 28

x = 28 - 12

x = 16

Sum of observations (numbers) = 5+6+7+x

Total number of observations (numbers) = how many numbers are in the observation. In this case 4, thus (5,6,7 and x)

Every number is divisible by 1

Re-write the equation

Simplify like terms and cross multiply to solve for the value of x

1 x (18+x) = 4 x 8

1 times any number is the same number, hence 1 x (18+x) = 18+x

4 x 8 = 32

18+x = 32

x = 32 - 18

x = 14

The median is the middle score in a set of given numbers.

The mean is the arithmetic average of a set of given numbers.

The mode is the most frequently occurring score in a set of given numbers.

Median

The median is the middle score of a distribution. To calculate the median
* Arrange your numbers in numerical order.
* Count how many numbers you have.
* If you have an odd number, divide by 2 and round up to get the position of the median number.
* If you have an even number, divide by 2. Go to the number in that position and average it with the number in the next higher position to get the median.

In the question above, there are 12 numbers. 12 is even and so to get the median position, divide 12 by 2, which falls on the 6th number.

The numbers are not ordered so you have to order them from the lowest to the highest before determining the 6th position

⇒ 4,16,13,18,3,20,6,7,15,2,10,12 = 2,3,4,6,7,10,12,13,15,16,18,20

The 6th number from the ordered numbers is 10

Since the total number count (12) is even, the median is the average of the 6th and its next number(7th number)

Average simply means the sum of the two numbers divided by 2

So the median will be the 6th number + the 7th number divided by 2

⇒ the median = (10+12)/2 = 22/2 = 11

If the total number count is odd, the median is simply the middle number in the ordered numbers

Mean

The mean, or average, is calculated by adding up the scores and dividing the total by the number of scores. Consider the following number set: 3, 4, 6, 6, 8, 9, 11.

The mean is calculated in the following manner:
3 + 4 + 6 + 6 + 8 + 9 + 11 = 47
number of scores is 7
⇒ The mean = 47 / 7 = 6.7

The mean (average) of the number set is 6.7.

Mode

Since the mode is the most frequently occurring score in a distribution, simply select the most common score as your mode.

Consider the following number distribution of 2, 3, 6, 3, 7, 5, 1, 2, 3, 9.

The mode of these numbers would be 3 since three(3) is the most frequently occurring number.

In some number sets, there may actually be two modes. This is known as bi-modal distribution and it occurs when there are two numbers that are tied in frequency.

For example, consider the following set of numbers: 13, 17, 20, 20, 21, 23, 23, 26, 29, 30.

In this set, both 20 and 23 occur twice.

If no number in a set occurs more than once, then there is no mode for that set of data.

NOTE:The pie chart is in percentage (%) and not in degree (^o).

Since its in percentage, the sum of all the percentages should add up to 100% (Thus percentage means out of 100)

If its in fraction, the sum of all the fractions must add up to 1

To get the degree out of a percentage or fraction, its simply the percentage or fraction x 360^o

Thus to get a value of a percentage or fraction out of a total, its simply the multiplication of the fraction or percentage by the total

Thus the degree for the INSURANCE AND TAXES will be the fraction or percentage of the INSURANCE AND TAXES by 360 (sum of all the angles in a pie chart is 360)

First you have to calculate the % of the INSURANCE AND TAXES

INSURANCE AND TAXES%+11%+3%+5%+16%+28%+22% = 100%

INSURANCE AND TAXES% + 85% = 100%

INSURANCE AND TAXES% = 100%-85%

INSURANCE AND TAXES% = 15%

Applying the rule of calculating for a value of fraction or percentage

Value = Fraction or Percentage x the total

The total angles is 360^o

The percentage of the INSURANCE AND TAXES% = 15%

⇒ INSURANCE AND TAXES^o = 15/100 x 360

NOTE:% means over 100 ⇒ 15% = 15/100

⇒ INSURANCE AND TAXES^o = 15/100 x 360^o = 5400/100 = 54^o

Formula

Value of a fraction or percentage of a total = fraction or percentage x the total

Thus to get a value of a percentage or fraction out of a total, its simply the multiplication of the fraction or percentage by the total

The percentage for clothing is 11%

The amount spent on clothing = Percentage of the clothing x the total amount (income)

⇒ Amount spent on clothing = 11/100 x 40,000 = 11 x 4000 = 44000

NOTE:% means over 100 ⇒ 11% = 11/100

8 appears three times, more than any other value.

To find the median, we need to arrange the marks in order and find the middle value.

Marks scored by the learners are:

0, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5

Note: the frequency shows how many times each mark was scored. For example, the mark 2 was scored 7 times, so we write 2 seven times.

There are 22 marks in total.

Locate the middle value(s). When there are two middle values, add them and divide by 2.

Middle values are the 11th and 12th values.

11th value = 3

12th value = 3

Median = $\frac{\mathrm{3\; +\; 3}}{2}$ = $\frac{6}{2}$ = 3

Note: if the dataset is huge, you have to use this formula to find the median position and sum the frequencies till you get to that position to use corresponding values to calculate the median.

If the position is decimal, there are two middle values and the position falls between the whole number and its next integer.

In the above case, the sum of frequencies will be:

1 + 2 + 7 + 5 + 4 + 3 = 22

Median position = $\frac{\mathrm{22\; +\; 1}}{2}$ = $\frac{23}{2}$ = 11.5

Since the position is 11.5, the middle values are the 11th and 12th values.

Sum the frequencies until you reach the 11th and 12th positions.

1 + 2 + 7 = 10

The 11th value is 3, and the 12th value is 3.

Median = $\frac{\mathrm{3\; +\; 3}}{2}$ = $\frac{6}{2}$ = 3

Number of possible selection = frequency of mark 2 = 7

Number of samples = total number of marks = 22

P(2) = $\frac{7}{22}$