1. An ultrasound system, comprising: an ultrasound data acquisition unit configured to sequentially acquire ultrasound data corresponding to a living body; and a processing unit, comprising: an ultrasound image forming section configured to form a plurality ultrasound image based on the ultrasound data; a determining section configured to compare a reference frame rate and a current frame rate to output a determining result; a coefficient estimating section including a resampling section and an estimating section and configured to output a frame average coefficient for image data in a frame average process based on the determining result, the resampling section being configured to resample an i th ultrasound image (i is a positive integer) and an i th frame average image at a sampling rate equal to the current frame rate based on the determining result to form first resampling data from the i th ultrasound image and to form second resampling data from the i th frame average image, the estimating section being configured to estimate the frame average coefficient based on the first resampling data and the second resampling data; and a frame average processing section configured to form an (i+1) th frame average image by performing the frame average process between the i th frame average image and an (i+1) th ultrasound image based on the frame average coefficient outputted from the coefficient estimating section, wherein the frame average processing section comprises: a first multiplying section configured to multiply the frame average coefficient with the first resampling data to output first multiplication data; a delaying section configured to apply a delay to the (i) th frame average image to output a delayed i th frame average image; a second multiplying section configured to multiply the frame average coefficient with the the delayed i th frame average image to output second multiplication data; and an adding section configured to add the first multiplication data and the second multiplication data to output the (i+1) th frame average image.