Question
Consider the following frequency table.
| x | Frequency |
| 1 | 12 |
| 3 | 20 |
| 6 | 26 |
| 9 | 32 |
| 11 | 5 |
(a) (i) Write down the mode.
(ii) Find the value of the range.
(b) Find the mean.
(ii) Find the variance.
Answer/Explanation
Ans:
a) (i) mode = 9
(ii) we have
range = max – min
= 11 – 1
= 10
(b) (i) Using the mean formula, we get
\(\bar{x}=\left [ \sum_{i=1}^{5} \right ]f_{i}x_{i}/\left [ \sum_{i=1}^{5} \right ]f_{i}\)
\(=\frac{(12)(1)+(20)(3)+(26)(6)+(32)(9)+(5)(11)}{12+20+26+32+5}\)
≈ 6.01
(ii) Using our G.D.C. to calculate the variance, σ2, we get
σ2 = (3.06592..)2
≈ 9.40
Question
Consider the expansion of (2x – 1)9.
(a) Write down the number of terms in this expansion.
(b) Find the coefficient of the term in x2.
Answer/Explanation
Ans:
(a) The number of terms in this expansion is 10
(b) The term in x2 is
\(\binom{9}{7}[(2x)^{9-7}][(-1)^{7}]=36[4x^{2}][-1]\)
= -144x2
Hence the coefficient of the term in x2 is – 144