Statistics
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PYQ से महत्वपूर्ण तथ्य
Kabbadi scores median: 17,2,7,27,15,5,14,8,10,24,48,10,8,7,18,28. Sorted median = (10+14)/2 = 12
12
What is the mean of 5, 8, 3, 10, 4, 6?
6
What is the median of 3, 5, 7, 9, 11?
7
What is the mode of 4, 2, 7, 4, 9, 4, 3?
4
If the range of a data set is 20 and the smallest value is 5, what is the largest value?
25
The average marks of 40 students in a class is 75. If one student's marks are changed from 35 to 75, what is the new ave
76
अध्ययन नोट्स
Measures of Central Tendency: Mean (average — sum of observations ÷ number of observations. For grouped data: Mean = Σfx/Σf where f=frequency, x=class mark), Median (middle value when data arranged in order — for odd n: (n+1)/2 th term, for even n: average of n/2 and (n/2+1) terms), Mode (most frequently occurring value — a dataset can have no mode, one mode, or multiple modes).
Mean for grouped frequency distribution — three methods: Direct Method (Σfx/Σf), Assumed Mean/Short-cut Method (A + Σfd/Σf, where d=x-A), Step Deviation Method (A + (Σfu/Σf)×h, where u=(x-A)/h). Step deviation is most efficient for large class intervals.
Median for grouped data: Median = l + [(n/2 - cf)/f] × h, where l=lower limit of median class, n=total frequency, cf=cumulative frequency before median class, f=frequency of median class, h=class width. Mode for grouped data: Mode = l + [(f₁-f₀)/(2f₁-f₀-f₂)] × h, where f₁=modal class frequency, f₀=preceding class frequency, f₂=succeeding class frequency.
Relationship: 3 Median = Mode + 2 Mean (empirical relationship). Measures of Dispersion: Range (highest - lowest), Mean Deviation, Variance, Standard Deviation (σ = √variance). Ogive: Cumulative frequency graph — 'less than' ogive (ascending) and 'more than' ogive (descending). Their intersection point gives the Median.
REET Exam Tips: 5 questions — focus on Mean-Median-Mode calculation formulas, the empirical relationship (3Median = Mode + 2Mean), and step deviation method. Word problems involve calculating mean/median from frequency tables.