- Nina weighed a random sample of 50 carrots from her shop and recorded the weight, in grams to the nearest gram, for each carrot. The results are summarised below.
| Weight of carrot | Frequency (f) | Weight midpoint \(( \boldsymbol { x }\) grams \()\) |
| \(45 - 54\) | 5 | 49.5 |
| \(55 - 59\) | 10 | 57 |
| \(60 - 64\) | 22 | 62 |
| \(65 - 74\) | 13 | 69.5 |
$$\text { (You may use } \sum \mathrm { f } x ^ { 2 } = 192102.5 \text { ) }$$
- Use linear interpolation to estimate the median weight of these carrots.
- Find an estimate for the mean weight of these carrots.
- Find an estimate for the standard deviation of the weights of these carrots.
A carrot is selected at random from Nina's shop.
- Estimate the probability that the weight of this carrot is more than 70 grams.