The number of quartiles of a distribution is:

3. Three quartiles divide the data into four equal parts.

The second quartile Q₂ is equal to the:

Median. Q₂ divides the data into two equal halves.

Median. The 5th decile is the middle value.

P₂₅ is the same as:

Q₁. 25% of observations lie below both.

P₇₅ is the same as:

Q₃. 75% of observations lie below Q₃.

Maharashtra State Board · HSC Commerce · Class 11 (Std XI)

Class 11 Maths and Statistics Part 2 Chapter 1: Partition Values

Short notes, key concepts, quick revision and practice MCQs with answers

Partition values divide an arranged set of observations into equal parts. The chapter computes quartiles, deciles and percentiles for raw data, discrete series and continuous frequency distributions, and locates them graphically with ogives.

Key concepts: Partition Values

Partition values: Values that divide a distribution into equal parts. The median divides it into 2 parts; quartiles into 4, deciles into 10 and percentiles into 100 equal parts.
Quartiles: Three quartiles Q₁ (lower), Q₂ (median) and Q₃ (upper). 25% of observations lie below Q₁ and 75% below Q₃.
Deciles and percentiles: Nine deciles D₁ to D₉ and ninety-nine percentiles P₁ to P₉₉. D₅ = P₅₀ = Q₂ = median; P₂₅ = Q₁ and P₇₅ = Q₃.
Raw data: Arrange in ascending order. Qᵢ = value of the i(n + 1)/4 th observation, Dᵢ = value of i(n + 1)/10 th, Pᵢ = value of i(n + 1)/100 th. For a fractional position, interpolate between neighbouring observations.
Discrete series: Find the cumulative frequencies and N. Qᵢ is the value of X whose c.f. is first equal to or greater than i(N + 1)/4.
Continuous series: Qᵢ = L + (h/f)(iN/4 − c.f.), Dᵢ = L + (h/f)(iN/10 − c.f.), Pᵢ = L + (h/f)(iN/100 − c.f.), where L is the lower boundary of the class, f its frequency, h its width and c.f. the cumulative frequency of the preceding class.
Graphical location (ogives): An ogive is a cumulative frequency curve. Plot less than c.f. against upper class boundaries (less than ogive) or more than c.f. against lower boundaries (more than ogive). The two ogives intersect at the median; other partition values are read from the less than ogive.

Quick revision: important points

Number of quartiles = 3, deciles = 9, percentiles = 99.
Q₂ = D₅ = P₅₀ = median.
Class containing Qᵢ: the first class whose c.f. ≥ iN/4.
Q₁ is the lower quartile and Q₃ is the upper quartile.
For raw data use (n + 1); for grouped continuous data use N without adding 1.
In a less than ogive, the X-axis carries upper class boundaries.

Practice MCQs with answers

The number of quartiles of a distribution is:
1. 2
2. 3
3. 4
4. 9
Show answer
Answer: B. 3
Three quartiles divide the data into four equal parts.
The second quartile Q₂ is equal to the:
1. Mean
2. Mode
3. Median
4. Range
Show answer
Answer: C. Median
Q₂ divides the data into two equal halves.
D₅ is equal to:
1. Q₁
2. Median
3. P₅
4. Q₃
Show answer
Answer: B. Median
The 5th decile is the middle value.
P₂₅ is the same as:
1. Q₁
2. Q₂
3. D₂
4. Q₃
Show answer
Answer: A. Q₁
25% of observations lie below both.
P₇₅ is the same as:
1. D₇
2. Q₃
3. Q₂
4. D₈
Show answer
Answer: B. Q₃
75% of observations lie below Q₃.

All Class 11 Maths and Statistics chapters

Class 11 Maths and Statistics notes: all chapters