Measures Of Dispersion — Flashcards
Telangana Open School (TOSS) · Class 12 · Mathematics
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Find the range of the data: 12, 18, 25, 30, 42, 50
Answer
Step 1: Identify the largest value = 50 Step 2: Identify the smallest value = 12 Step 3: Range = Largest - Smallest = 50 - 12 = 38 Answer: 38…
The marks of 5 students are: 65, 70, 75, 80, 85. Find the mean deviation from the mean.
Answer
Step 1: Calculate mean = (65+70+75+80+85)/5 = 375/5 = 75 Step 2: Find deviations from mean: |65-75|=10, |70-75|=5, |75-75|=0, |80-75|=5, |85-75|=10 Step 3: Sum of absolute deviations = 10+5+0+5+10 = 3…
Calculate the variance and standard deviation of the data: 2, 4, 6, 8, 10
Answer
Step 1: Mean = (2+4+6+8+10)/5 = 30/5 = 6 Step 2: Squared deviations: (2-6)²=16, (4-6)²=4, (6-6)²=0, (8-6)²=4, (10-6)²=16 Step 3: Sum of squared deviations = 16+4+0+4+16 = 40 Step 4: Variance = 40/5 = …
For the data: 5, 8, 12, 15, 20, find the mean deviation from the median.
Answer
Step 1: Arrange data: 5, 8, 12, 15, 20 (already sorted) Step 2: Median = middle value = 12 Step 3: Absolute deviations from median: |5-12|=7, |8-12|=4, |12-12|=0, |15-12|=3, |20-12|=8 Step 4: Sum of a…
When do you use mean deviation instead of standard deviation?
Answer
Mean deviation is used when you want a simple measure of average spread that is less affected by extreme values. It's easier to understand and calculate. Standard deviation is preferred in statistical…
Why is the sum of deviations from the mean always zero?
Answer
Because the mean is the balancing point of the data. Positive deviations (values above mean) exactly cancel out negative deviations (values below mean). For example, in data 2,4,6: mean=4, deviations …
Formula for mean deviation from mean for ungrouped data
Answer
Formula: MD = (Σ|xᵢ - x̄|) / n Where: x̄ = mean of data xᵢ = individual observations n = number of observations | | = absolute value Example: For data 3,5,7: mean=5, MD=(|3-5|+|5-5|+|7-5|)/3=(2+0+2)/3…
The daily wages (in Rs) of 6 workers are: 100, 120, 140, 160, 180, 200. Find the range and coefficient of range.
Answer
Step 1: Largest value = 200, Smallest value = 100 Step 2: Range = 200 - 100 = 100 Step 3: Coefficient of range = (L-S)/(L+S) = (200-100)/(200+100) = 100/300 = 1/3 ≈ 0.333 Answer: Range = 100, Coeffici…
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