Question

1. Find x and y so that the ordered data set has a mean of 42 and a median of 35. 

17, 22, 26, 29,x,42,67,70,y

2. The exam grades of 7 students are given below. 70, 66, 72, 96, 46, 90, 50 

            Find 

1. Mean 
2. The standard deviation 

Answer 1

1. So, as we see from the ordered data median = x = 35

$42 = \frac{14+22+26+29+35+42+67+70 +y}{9} \\ 42 \times 9 = 305+y \\ 378 - 305 = y \\ y=73$

2.

$Mean = \frac{70+66+72+96+46+90+50}{7}= 70 \\ Var = \frac{1}{7-1}((70-70)^2+(66-70)^2+(72-70)^2+(96-70)^2+(46-70)^2+(90-70)^2+(50-70)^2 ) \\ = \frac{1}{6}( 0+16+4+676+400+400) \\ = \frac{1496}{6} \\ = 249.33 \\ SD = \sqrt{Var} \\ = \sqrt{249.33} \\ =15.79$