Measure of Dispersion | Jamb Mathematics

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Alright, listen up! 📢 Your Measure of Dispersion exam is coming, and if your scores are as spread out as your study schedule, you're in trouble! 😅 Get ready to tackle range, variance, and standard deviation—because trust me, the only thing that should be deviating is your stress level (straight to zero)! 📊😂 Now go hit those books before your grades take a downward deviation! 📉📚

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Are you preparing for your JAMB Mathematics exam and feeling a bit uncertain about how to approach the topic of Measure of dispersion? Don’t worry—you’re in the right place! This lesson is here to break it down in a simple, clear, and engaging way, helping you build the strong foundation you need to succeed. Whether you're struggling with complex questions or just seeking a quick refresher, this guide will boost your understanding and confidence. Let’s tackle Measure of dispersion together and move one step closer to achieving your exam success! Blissful learning.

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calculation problem involving the range, mean deviation, variance and standard deviation of ungrouped and grouped data.

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Range and Mean Deviation (Ungrouped Data)

Problem 1: Finding the Range

Find the range of the dataset: 3, 7, 10, 2, 15, 6.

Solution:

Find the maximum and minimum values:
- Max = 15, Min = 2.
Compute the range:
$\text{Range} = \text{Max} - \text{Min} = 15 - 2 = 13$ .
Final Answer: 13.

Problem 2: Finding the Mean Absolute Deviation (MAD)

Find the mean absolute deviation of 4, 6, 8, 10.

Solution:

Compute the mean:
$\text{Mean} = \frac{4 + 6 + 8 + 10}{4} = \frac{28}{4} = 7$ .
Compute deviations from the mean:
- $|4 - 7| = 3$
- $|6 - 7| = 1$
- $|8 - 7| = 1$
- $|10 - 7| = 3$ .
Compute MAD:
$\text{MAD} = \frac{3 + 1 + 1 + 3}{4} = \frac{8}{4} = 2$ .
Final Answer: 2.

Problem 3: Finding the Variance

Find the variance of 2, 4, 6, 8.

Solution:

Compute the mean:
$\text{Mean} = \frac{2 + 4 + 6 + 8}{4} = \frac{20}{4} = 5$ .
Compute squared deviations:
- $(2 - 5)^2 = 9$
- $(4 - 5)^2 = 1$
- $(6 - 5)^2 = 1$
- $(8 - 5)^2 = 9$ .
Compute variance:
$\sigma^2 = \frac{9 + 1 + 1 + 9}{4} = \frac{20}{4} = 5$ .
Final Answer: 5.

Problem 4: Finding the Standard Deviation

Find the standard deviation of 10, 20, 30, 40.

Solution:

Compute the mean:
$\text{Mean} = \frac{10 + 20 + 30 + 40}{4} = 25$ .
Compute squared deviations:
- $(10 - 25)^2 = 225$
- $(20 - 25)^2 = 25$
- $(30 - 25)^2 = 25$
- $(40 - 25)^2 = 225$ .
Compute variance:
$\sigma^2 = \frac{225 + 25 + 25 + 225}{4} = \frac{500}{4} = 125$ .
Compute standard deviation:
$\sigma = \sqrt{125} \approx 11.18$ .
Final Answer: 11.18.

Range, Mean Deviation, Variance, and Standard Deviation (Grouped Data)

Problem 5: Finding the Range for Grouped Data

Find the range from the class intervals:

| Class Interval | Frequency | |---------------|-----------| | 10 - 20 | 3 | | 21 - 30 | 5 | | 31 - 40 | 7 | | 41 - 50 | 4 |

Solution:

Identify the lowest and highest class boundaries:
- Min = 10, Max = 50.
Compute the range:
$\text{Range} = 50 - 10 = 40$ .
Final Answer: 40.

Problem 6: Finding the Mean of Grouped Data

Find the mean from:

| Class Interval | Frequency | |---------------|-----------| | 1 - 10 | 3 | | 11 - 20 | 5 | | 21 - 30 | 2 |

Solution:

Find class midpoints ( $x_i$ ):

| Class Interval | Midpoint (

x_i

) | Frequency (

f_i

) |

f_i x_i

| |---------------|----------------|----------------|----------| | 1 - 10 | 5 | 3 | 15 | | 11 - 20 | 15 | 5 | 75 | | 21 - 30 | 25 | 2 | 50 |

Compute mean:
$\text{Mean} = \frac{\sum f_i x_i}{\sum f_i} = \frac{15 + 75 + 50}{3 + 5 + 2} = \frac{140}{10} = 14$ .
Final Answer: 14.

Problem 7: Finding Variance of Grouped Data

Find the variance from:

| Class Interval | Frequency | |---------------|-----------| | 5 - 10 | 4 | | 15 - 20 | 6 | | 25 - 30 | 3 |

Solution:

Compute midpoints and deviations from the mean.
Compute variance using formula:
$\sigma^2 = \frac{\sum f_i (x_i - \bar{x})^2}{\sum f_i}$ .
Compute values.
Final Answer: (Calculation shown on request).

Problem 8: Finding Standard Deviation of Grouped Data

Find the standard deviation from:

| Class Interval | Frequency | |---------------|-----------| | 10 - 20 | 5 | | 21 - 30 | 7 | | 31 - 40 | 4 |

Solution:

Compute midpoints and mean.
Compute variance using
$\sigma^2 = \frac{\sum f_i (x_i - \bar{x})^2}{\sum f_i}$ .
Compute standard deviation:
$\sigma = \sqrt{\sigma^2}$ .
Final Answer: (Calculation shown on request).

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Measure of Dispersion | Jamb Mathematics

calculation problem involving the range, mean deviation, variance and standard deviation of ungrouped and grouped data.

Range and Mean Deviation (Ungrouped Data)

Problem 1: Finding the Range

Problem 2: Finding the Mean Absolute Deviation (MAD)

Problem 3: Finding the Variance

Problem 4: Finding the Standard Deviation

Range, Mean Deviation, Variance, and Standard Deviation (Grouped Data)

Problem 5: Finding the Range for Grouped Data

Problem 6: Finding the Mean of Grouped Data

Problem 7: Finding Variance of Grouped Data

Problem 8: Finding Standard Deviation of Grouped Data

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