# GRE® Math Practice | Statistics & Averages #5

#### GRE Questions | Mean & Median - Minimum Average

The GRE maths sample question given below is a problem solving question in statistics. Concept covered: Average (arithmetic mean) and median.

Question 5 :If the median of -10, 29, 6, 11, 31, and x is 20. What is the least possible average of the 6 numbers?

1. 16$$frac{1}{3}$ 2. 16$\frac{2}{3}$ 3. 16$\frac{1}{6}$ 4. 16 5. 11$\frac{1}{6}$ ## Get to 170 in GRE Quant #### Online GRE Courses From INR 2999 ### Video Explanation ## GRE Live Online Classes #### Starts Fri, August 26, 2022 ### Explanatory Answer | GRE Averages Practice Question 5 #### Given Data: Including x, we have a total of 6 numbers. So, Median = $\frac{\text{3rd term + 4th term}}{2}$ = $\frac{t_3 + t_4}{2}$ It is given that median = 20 So, $\frac{t_3 + t_4}{2}$ = 20 Or t3 + t4 = 40 #### Compute the least possible value for x: The only unknown is x. The average of all 6 numbers will be least if the value of x is at its least. The ascending order of the known values is -10, 6, 11, 29, 31. x has to be arranged in ascending order along with the other 5 numbers -10, 6, 11, 29, 31. x can take differet values. So, check for the different possibilities that satisifes the condition that the median is 20. #### Possibility 1: x ≤ 11 If x takes any value that is less than or equal to 11, then t4 will be 11. So, t3 ≤ 11 Then, t3 + t4 ≤ 22. Does not satisfy the condition that t3 + t4 = 40 #### Possibility 2: 11 < x < 29 If x takes any value that is greater than 11 but less than 29, then the order of the 6 numbers will be -10, 6, 11, x, 29, 31 The value of t3 = 11 and t4 = x The maximum possible value of t4 < 29 Therefore, t3 + t4 < 40. The given condition is not satisfied. #### Possibility 3: x ≥ 29 If x takes a value that is 29 or upwards, then three different possibilities exist. -10, 6, 11, 29, 29, 31$or) -10, 6, 11, 29, x, 31 (or) -10, 6, 11, 29, 31, x
In all 3 possibilities, notice that the value of t3 = 11 and t4 = 29.
So, the condition t3 + t4 = 40 gets satisfied in all three cases.
Among all three possibilities that work, the least possible value for x is 29 (1st of the 3 possibilities).

#### Compute the least possible average

Average = $$frac{\text{Sum of all observations}}{\text{Total number of observations}}$ Average of the given 6 numbers = $\frac{−10 + 6 + 11 + 29 + 29 + 31}{6}$ = $\frac{96}{6}$ = 16 Therefore, the least possible average of the 6 numbers = 16 #### Choice D is the correct answer #### GRE Online Course - QuantTry it free! Register in 2 easy steps and Start learning in 5 minutes! #### Already have an Account? #### GRE Live Online Classes Next Batch August 26, 2022 ##### Where is Wizako located? Wizako - GMAT, GRE, SAT Prep An Ascent Education Initiative 14B/1 Dr Thirumurthy Nagar 1st Street Nungambakkam Chennai 600 034. India Work @ Wizako ##### How to reach Wizako? Mobile:$91) 94451 58484
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