Types Of Central Tendency, Merits And Demerits And Simple Application: - SS1 Economics Lesson Note

The types of central tendency being discussed include: Mean, Mode and Median.

MEAN: The mean is a commonly used measure of central tendency. The mean is the sum of all the values in a dataset divided by the total number of values. The mean is a commonly used measure of central tendency as it considers all values in the dataset. It is sensitive to outliers and extreme values, which can greatly affect its value.

Merits:

• It is widely used and easily understood

It uses all the data points in the dataset, giving a more accurate representation of the data as a whole

Demerits:

• It is sensitive to outliers or extreme values and can be skewed by them.

It cannot be calculated for qualitative or categorical data

 

MEDIAN: The median is a measure of central tendency that is not affected by extreme values. The median is the value that separates the upper and lower half of a dataset. It is useful when there are outliers or extreme values in the dataset, as it is not affected by them.

Merits:

• It is not affected by outliers or extreme values in the dataset.

It can be used with both quantitative and qualitative data.

Demerits:

• It may not represent the true center of the data if there are only a few data points in the dataset.

It can be difficult to calculate for datasets with a large number of values.

 

MODE: The mode is the most frequent value in a dataset. The mode is the value that appears most frequently in a dataset. It is useful when determining the most common value in a set of data. The mode is not affected by outliers or extreme values and can be used with any type of data.

Merits:

• It is not affected by outliers or extreme values in the dataset

It can be used with any type of data, including categorical data.

Demerits:

• It may not exist or may be non-unique if no value appears more than once in the dataset.

It does not take into account all the values in the dataset.

 

Example problem:

Given a set of  10 numbers: 3, 4, 5, 7, 8, 4, 5, 9 ,2, 3. In simple sentences, find the:

i. Mean

ii. Mode

III. Median

Solution:

i. Mean: To find the mean of a set of numbers, we add all the numbers and divide by the total number of items in the set.

Mean = (3+4+5+7+8+4+5+9+2+3) / 10 = 50 / 10 = 5

Therefore, the mean of the given set of numbers is 5.

ii. Mode: The mode is the number that occurs most frequently in a set of numbers. In the given set of numbers, we can see that the numbers 3 and 4 each appear twice, and all other numbers appear only once. Therefore, both 3 and 4 are modes of this set.

iii. Median: To find the median of a set of numbers, we first arrange the numbers in ascending or descending order, and then find the middle number. If there are an even number of items in the set, we find the average of the two middle numbers.

Arranging the numbers in ascending order: 2, 3, 3, 4, 4, 5, 5, 7, 8, 9

The middle number is 5, so the median of the given set of numbers is 5.

Therefore, the mean of the given set of numbers is 5, the modes are 3 and 4, and the median is 5

 

Word problems on mean, median and mode:

1. A coffee shop sells three sizes of coffee: small, medium, and large. The prices of the coffees are $2, $3, and $4 respectively. Yesterday, the shop sold 20 small coffees, 15 medium coffees, and 10 large coffees. What is the mean price of a coffee sold by the shop yesterday?

Solution:

To find the mean price of a coffee sold by the shop yesterday, we need to calculate the total revenue and divide it by the total number of coffees sold:

Total revenue = (20 x $2) + (15 x $3) + (10 x $4) = $40 + $45 + $40 = $125

Total number of coffees sold = 20 + 15 + 10 = 45

Mean price of a coffee sold = $125 / 45 = $2.78 (rounded to two decimal places)

Therefore, the mean price of a coffee sold by the shop yesterday is $2.78.

 

1. The heights (in cm) of 7 students in a class are: 165, 170, 155, 175, 160, 155, 165. What is the median height of the students?

Solution:

To find the median height of the students, we first need to arrange the heights in ascending order:

155, 155, 160, 165, 165, 170, 175

Since there are an odd number of heights, the median is the middle value. In this case, the middle value is 165. Therefore, the median height of the students is 165 cm.

 

1.  In a class of 20 students, the number of siblings each student has is recorded. The results are: 1, 2, 2, 3, 0, 1, 0, 2, 1, 1, 0, 1, 2, 2, 0, 0, 3, 2, 1, 1. What is the mode of the number of siblings?

Solution:

To find the mode of the number of siblings, we need to find the number that appears most frequently. In this case, the number 1 appears 6 times, which is more than any other number. Therefore, the mode of the number of siblings is 1.