Variance and Standard Deviation

JEE Main Mathematics · Statistics · 39 questions, latest first

• Let the mean and the variance of seven observations 2,4, α, 8, β, 12,14, α<β, be 8 and 16 respectively. Then the quadratic…20266 April, Shift 2 · Q8
• A data consists of 20 observations x_1, x_2, …, x_20. If Σ_i=1^20(x_i+5)^2=2500 and Σ_i=1^20(x_i-5)^2=100, then the ratio of mean…20266 April, Shift 1 · Q9
• For 10 observations x_1, x_2, …, x_10, if Σ_i=1^10(x_i+2)^2=180 and Σ_i=1^10(x_i-1)^2=90, then their standard deviation is:20264 April, Shift 2 · Q8
• The mean and variance of n observations are 8 and 16, respectively. If the sum of the first ( n-1 ) observations is 48 and the…20262 April, Shift 2 · Q9
• Let X={x ∈ N: 1 ≤ x ≤ 19} and for some a, b ∈ R, Y={a x+b: x ∈ X}. If the mean and variance of the elements of Y are 30 and 750,…202624 January, Shift 2 · Q9
• The mean and variance of a data of 10 observations are 10 and 2, respectively. If an observations α in this data is replaced by…202624 January, Shift 1 · Q8
• If the mean and the variance of the data are μ and 19 respectively, then the value of λ+μ is202623 January, Shift 2 · Q9
• Let the mean and variance of 8 numbers -10,-7,-1, x, y, 9,2,16 be 7/2 and 293/4, respectively. Then the mean of 4 numbers x, y,…202623 January, Shift 1 · Q8
• The mean and standard deviation of 100 observations are 40 and 5.1, respectively. By mistake one observation is taken as 50…20257 April, Shift 1 · Q9
• Let the Mean and Variance of five observations x_1=1, x_2=3, x_3=a, x_4=7 and x_5=b, a>b, be 5 and 10 respectively. Then the…20253 April, Shift 2 · Q9
• If the mean and the variance of 6,4, a, 8, b, 12,10,13 are 9 and 9.25 respectively, then a+b+ab is equal to:20252 April, Shift 2 · Q8
• Let x_1, x_2, …., x_10 be ten observations such that Σ_i=1^10(x_i-2)=30, Σ_i=1^10(x_i-β)^2=98, β>2, and their variance is 4/5. If…202529 January, Shift 1 · Q9
• For a statistical data x_1, x_2, …, x_10 of 10 values, a student obtained the mean as 5.5 and Σ_i=1^10 x_i^2=371. He later found…202524 January, Shift 1 · Q7
• The variance of the numbers 8,21,34,47, …, 320 is ____.202523 January, Shift 2 · Q24
• If the variance of the frequency distribution is 160, then the value of c ∈ N is20249 April, Shift 2 · Q19
• Let a, b, c ∈ N and a<b<c. Let the mean, the mean deviation about the mean and the variance of the 5 observations 9,25, a, b, c…20248 April, Shift 2 · Q30
• The mean and standard deviation of 20 observations are found to be 10 and 2, respectively. On rechecking, it was found that an…20246 April, Shift 1 · Q18
• Consider 10 observations x_1, x_2, …, x_10 such that Σ_i=1^10(x_i-α)=2 and Σ_i=1^10(x_i-β)^2=40, where α, β are positive…20241 February, Shift 2 · Q19
• Let the mean and the variance of 6 observations a, b, 68,44,48,60 be 55 and 194, respectively. If a>b, then a+3 b is202431 January, Shift 2 · Q18
• The variance σ^2 of the data is ____.202430 January, Shift 2 · Q30
• If the mean and variance of five observations are 24/5 and 194/25 respectively and the mean of the first four observations is…202429 January, Shift 2 · Q18
• If the mean and variance of the data 65,68,58,44,48,45,60, α, β, 60 where α> β, are 56 and 66.2 respectively, then α^2+β^2 is…202429 January, Shift 1 · Q30
• The mean and standard deviation of 15 observations were found to be 12 and 3 respectively. On rechecking it was found that an…202427 January, Shift 2 · Q30
• Let a_1, a_2, … a_10 be 10 observations such that Σ_k=1^10 a_k=50 and Σ_∀ k<j a_k. a_j=1100. Then the standard deviation of a_1,…202427 January, Shift 1 · Q20
• The mean and standard deviation of 10 observations are 20 and 8 respectively. Later on, it was observed that one observation was…202315 April, Shift 1 · Q19
• The mean and standard deviation of the marks of 10 students were found to be 50 and 12 respectively. Later, it was observed that…202313 April, Shift 2 · Q29
• Let the mean of the data be 5. If m and σ^2 are respectively the mean deviation about the mean and the variance of the data, then…202313 April, Shift 1 · Q29
• Let the positive numbers a_1, a_2, a_3, a_4 and a_5 be in a G.P. Let their mean and variance be 31/10 and m/n respectively, where…202312 April, Shift 1 · Q24
• Let μ be the mean and σ be the standard deviation of the distribution where Σ f_i=62. If [x] denotes the greatest integer ≤ x,…202310 April, Shift 2 · Q19
• If the mean of the frequency distribution is 28, then its variance is ____.202310 April, Shift 1 · Q30
• Let the mean and variance of 12 observations be 9/2 and 4 respectively. Later on, it was observed that two observations were…20238 April, Shift 2 · Q18
• Let the mean and variance of 8 numbers x, y, 10,12,6,12,4,8 be 9 and 9.25 respectively. If x>y, then 3 x-2 y is equal to ____.20238 April, Shift 1 · Q30
• If the mean and variance of the frequency distribution are 9 and 15.08 respectively, then the value of α^2+β^2-α β is ____.20236 April, Shift 2 · Q29
• Let 9=x_1<x_2<…<x_7 be in an A.P. with common difference d. If the standard deviation of x_1, x_2 …, x_7 is 4 and the mean is x̄,…20231 February, Shift 2 · Q77
• The mean and variance of 5 observations are 5 and 8 respectively. If 3 observations are 1,3,5, then the sum of cubes of the…20231 February, Shift 1 · Q78
• If the variance of the frequency distribution is 3, then α is equal to ____.202331 January, Shift 1 · Q89
• The mean and variance of 7 observations are 8 and 16 respectively. If one observation 14 is omitted and a and b are respectively…202330 January, Shift 1 · Q89
• The mean and variance of the marks obtained by the students in a test are 10 and 4 respectively. Later, the marks of one of the…202325 January, Shift 1 · Q77
• Let the six numbers a_1, a_2, a_3, a_4, a_5, a_6, be in A.P. and a_1+a_3=10. If the mean of these six numbers is 19/2 and their…202324 January, Shift 2 · Q79